How to find the volume of a tetrahedron - PSAT Math

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Question

Note: Figure NOT drawn to scale.

The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

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Answer

We are looking for the height of the pyramid.

The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows:

$B = $$\frac{s^{2}$$ $\sqrt{3}$ }{4}$

$B = $$\frac{4^{2}$$ $\sqrt{3}$ }{4}$

$B = $\frac{16 \sqrt{3}$ }{4}$

$B = 4$\sqrt{3}$$

The height of a pyramid can be calculated using the fomula

$V = $\frac{1}{3}$Bh$

We set and $B = 4$\sqrt{3}$$ and solve for :

$$\frac{1}{3}$ \cdot 4$\sqrt{3}$ \cdot h = 25$

$h = $\frac{25 \cdot 3}{4 \sqrt{3}$} = $\frac{75}{4 \sqrt{3}$} \approx $\frac{75}{4 \cdot 1.7321}$ \approx 10.8$

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Question

Note: Figure NOT drawn to scale.

Give the volume (nearest tenth) of the above triangular pyramid.

Tap to reveal answer

Answer

The height of the pyramid is . The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows:

$B = $$\frac{s^{2}$$ $\sqrt{3}$ }{4}$

$B = $$\frac{4^{2}$$ $\sqrt{3}$ }{4}$

$B = $\frac{16 \sqrt{3}$ }{4}$

$B = 4$\sqrt{3}$$

The volume of a pyramid can be calculated using the fomula

$V = $\frac{1}{3}$Bh$

$V = $\frac{1}{3}$ \cdot 4$\sqrt{3}$ \cdot 8 = $\frac{32\sqrt{3}$ }{3} \approx $\frac{32 \cdot 1.7321}{3}$ \approx 18.5$

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Question

A regular tetrahedron has an edge length of . What is its volume?

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Answer

The volume of a tetrahedron is found with the equation , where represents the length of an edge of the tetrahedron.

Plug in 4 for the edge length and reduce as much as possible to find the answer:

$V=\frac{64}{6\sqrt{2}$}$

$V=\frac{32}{3\sqrt{2}$}$

The volume of the tetrahedron is $$\frac{32}{3\sqrt{2}$}$ .

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Question

Note: Figure NOT drawn to scale.

The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

Tap to reveal answer

Answer

We are looking for the height of the pyramid.

The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows:

$B = $$\frac{s^{2}$$ $\sqrt{3}$ }{4}$

$B = $$\frac{4^{2}$$ $\sqrt{3}$ }{4}$

$B = $\frac{16 \sqrt{3}$ }{4}$

$B = 4$\sqrt{3}$$

The height of a pyramid can be calculated using the fomula

$V = $\frac{1}{3}$Bh$

We set and $B = 4$\sqrt{3}$$ and solve for :

$$\frac{1}{3}$ \cdot 4$\sqrt{3}$ \cdot h = 25$

$h = $\frac{25 \cdot 3}{4 \sqrt{3}$} = $\frac{75}{4 \sqrt{3}$} \approx $\frac{75}{4 \cdot 1.7321}$ \approx 10.8$

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Question

Note: Figure NOT drawn to scale.

Give the volume (nearest tenth) of the above triangular pyramid.

Tap to reveal answer

Answer

The height of the pyramid is . The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows:

$B = $$\frac{s^{2}$$ $\sqrt{3}$ }{4}$

$B = $$\frac{4^{2}$$ $\sqrt{3}$ }{4}$

$B = $\frac{16 \sqrt{3}$ }{4}$

$B = 4$\sqrt{3}$$

The volume of a pyramid can be calculated using the fomula

$V = $\frac{1}{3}$Bh$

$V = $\frac{1}{3}$ \cdot 4$\sqrt{3}$ \cdot 8 = $\frac{32\sqrt{3}$ }{3} \approx $\frac{32 \cdot 1.7321}{3}$ \approx 18.5$

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Question

A regular tetrahedron has an edge length of . What is its volume?

Tap to reveal answer

Answer

The volume of a tetrahedron is found with the equation , where represents the length of an edge of the tetrahedron.

Plug in 4 for the edge length and reduce as much as possible to find the answer:

$V=\frac{64}{6\sqrt{2}$}$

$V=\frac{32}{3\sqrt{2}$}$

The volume of the tetrahedron is $$\frac{32}{3\sqrt{2}$}$ .

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Question

Note: Figure NOT drawn to scale.

The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

Tap to reveal answer

Answer

We are looking for the height of the pyramid.

The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows:

$B = $$\frac{s^{2}$$ $\sqrt{3}$ }{4}$

$B = $$\frac{4^{2}$$ $\sqrt{3}$ }{4}$

$B = $\frac{16 \sqrt{3}$ }{4}$

$B = 4$\sqrt{3}$$

The height of a pyramid can be calculated using the fomula

$V = $\frac{1}{3}$Bh$

We set and $B = 4$\sqrt{3}$$ and solve for :

$$\frac{1}{3}$ \cdot 4$\sqrt{3}$ \cdot h = 25$

$h = $\frac{25 \cdot 3}{4 \sqrt{3}$} = $\frac{75}{4 \sqrt{3}$} \approx $\frac{75}{4 \cdot 1.7321}$ \approx 10.8$

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Question

Note: Figure NOT drawn to scale.

Give the volume (nearest tenth) of the above triangular pyramid.

Tap to reveal answer

Answer

The height of the pyramid is . The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows:

$B = $$\frac{s^{2}$$ $\sqrt{3}$ }{4}$

$B = $$\frac{4^{2}$$ $\sqrt{3}$ }{4}$

$B = $\frac{16 \sqrt{3}$ }{4}$

$B = 4$\sqrt{3}$$

The volume of a pyramid can be calculated using the fomula

$V = $\frac{1}{3}$Bh$

$V = $\frac{1}{3}$ \cdot 4$\sqrt{3}$ \cdot 8 = $\frac{32\sqrt{3}$ }{3} \approx $\frac{32 \cdot 1.7321}{3}$ \approx 18.5$

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Question

A regular tetrahedron has an edge length of . What is its volume?

Tap to reveal answer

Answer

The volume of a tetrahedron is found with the equation , where represents the length of an edge of the tetrahedron.

Plug in 4 for the edge length and reduce as much as possible to find the answer:

$V=\frac{64}{6\sqrt{2}$}$

$V=\frac{32}{3\sqrt{2}$}$

The volume of the tetrahedron is $$\frac{32}{3\sqrt{2}$}$ .

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Question

Note: Figure NOT drawn to scale.

The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

Tap to reveal answer

Answer

We are looking for the height of the pyramid.

The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows:

$B = $$\frac{s^{2}$$ $\sqrt{3}$ }{4}$

$B = $$\frac{4^{2}$$ $\sqrt{3}$ }{4}$

$B = $\frac{16 \sqrt{3}$ }{4}$

$B = 4$\sqrt{3}$$

The height of a pyramid can be calculated using the fomula

$V = $\frac{1}{3}$Bh$

We set and $B = 4$\sqrt{3}$$ and solve for :

$$\frac{1}{3}$ \cdot 4$\sqrt{3}$ \cdot h = 25$

$h = $\frac{25 \cdot 3}{4 \sqrt{3}$} = $\frac{75}{4 \sqrt{3}$} \approx $\frac{75}{4 \cdot 1.7321}$ \approx 10.8$

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Question

Note: Figure NOT drawn to scale.

Give the volume (nearest tenth) of the above triangular pyramid.

Tap to reveal answer

Answer

The height of the pyramid is . The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows:

$B = $$\frac{s^{2}$$ $\sqrt{3}$ }{4}$

$B = $$\frac{4^{2}$$ $\sqrt{3}$ }{4}$

$B = $\frac{16 \sqrt{3}$ }{4}$

$B = 4$\sqrt{3}$$

The volume of a pyramid can be calculated using the fomula

$V = $\frac{1}{3}$Bh$

$V = $\frac{1}{3}$ \cdot 4$\sqrt{3}$ \cdot 8 = $\frac{32\sqrt{3}$ }{3} \approx $\frac{32 \cdot 1.7321}{3}$ \approx 18.5$

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Question

A regular tetrahedron has an edge length of . What is its volume?

Tap to reveal answer

Answer

The volume of a tetrahedron is found with the equation , where represents the length of an edge of the tetrahedron.

Plug in 4 for the edge length and reduce as much as possible to find the answer:

$V=\frac{64}{6\sqrt{2}$}$

$V=\frac{32}{3\sqrt{2}$}$

The volume of the tetrahedron is $$\frac{32}{3\sqrt{2}$}$ .

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Question

Note: Figure NOT drawn to scale.

The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

Tap to reveal answer

Answer

We are looking for the height of the pyramid.

The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows:

$B = $$\frac{s^{2}$$ $\sqrt{3}$ }{4}$

$B = $$\frac{4^{2}$$ $\sqrt{3}$ }{4}$

$B = $\frac{16 \sqrt{3}$ }{4}$

$B = 4$\sqrt{3}$$

The height of a pyramid can be calculated using the fomula

$V = $\frac{1}{3}$Bh$

We set and $B = 4$\sqrt{3}$$ and solve for :

$$\frac{1}{3}$ \cdot 4$\sqrt{3}$ \cdot h = 25$

$h = $\frac{25 \cdot 3}{4 \sqrt{3}$} = $\frac{75}{4 \sqrt{3}$} \approx $\frac{75}{4 \cdot 1.7321}$ \approx 10.8$

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Question

Note: Figure NOT drawn to scale.

Give the volume (nearest tenth) of the above triangular pyramid.

Tap to reveal answer

Answer

The height of the pyramid is . The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows:

$B = $$\frac{s^{2}$$ $\sqrt{3}$ }{4}$

$B = $$\frac{4^{2}$$ $\sqrt{3}$ }{4}$

$B = $\frac{16 \sqrt{3}$ }{4}$

$B = 4$\sqrt{3}$$

The volume of a pyramid can be calculated using the fomula

$V = $\frac{1}{3}$Bh$

$V = $\frac{1}{3}$ \cdot 4$\sqrt{3}$ \cdot 8 = $\frac{32\sqrt{3}$ }{3} \approx $\frac{32 \cdot 1.7321}{3}$ \approx 18.5$

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Question

A regular tetrahedron has an edge length of . What is its volume?

Tap to reveal answer

Answer

The volume of a tetrahedron is found with the equation , where represents the length of an edge of the tetrahedron.

Plug in 4 for the edge length and reduce as much as possible to find the answer:

$V=\frac{64}{6\sqrt{2}$}$

$V=\frac{32}{3\sqrt{2}$}$

The volume of the tetrahedron is $$\frac{32}{3\sqrt{2}$}$ .

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Question

Note: Figure NOT drawn to scale.

The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

Tap to reveal answer

Answer

We are looking for the height of the pyramid.

The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows:

$B = $$\frac{s^{2}$$ $\sqrt{3}$ }{4}$

$B = $$\frac{4^{2}$$ $\sqrt{3}$ }{4}$

$B = $\frac{16 \sqrt{3}$ }{4}$

$B = 4$\sqrt{3}$$

The height of a pyramid can be calculated using the fomula

$V = $\frac{1}{3}$Bh$

We set and $B = 4$\sqrt{3}$$ and solve for :

$$\frac{1}{3}$ \cdot 4$\sqrt{3}$ \cdot h = 25$

$h = $\frac{25 \cdot 3}{4 \sqrt{3}$} = $\frac{75}{4 \sqrt{3}$} \approx $\frac{75}{4 \cdot 1.7321}$ \approx 10.8$

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Question

Note: Figure NOT drawn to scale.

Give the volume (nearest tenth) of the above triangular pyramid.

Tap to reveal answer

Answer

The height of the pyramid is . The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows:

$B = $$\frac{s^{2}$$ $\sqrt{3}$ }{4}$

$B = $$\frac{4^{2}$$ $\sqrt{3}$ }{4}$

$B = $\frac{16 \sqrt{3}$ }{4}$

$B = 4$\sqrt{3}$$

The volume of a pyramid can be calculated using the fomula

$V = $\frac{1}{3}$Bh$

$V = $\frac{1}{3}$ \cdot 4$\sqrt{3}$ \cdot 8 = $\frac{32\sqrt{3}$ }{3} \approx $\frac{32 \cdot 1.7321}{3}$ \approx 18.5$

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Question

A regular tetrahedron has an edge length of . What is its volume?

Tap to reveal answer

Answer

The volume of a tetrahedron is found with the equation , where represents the length of an edge of the tetrahedron.

Plug in 4 for the edge length and reduce as much as possible to find the answer:

$V=\frac{64}{6\sqrt{2}$}$

$V=\frac{32}{3\sqrt{2}$}$

The volume of the tetrahedron is $$\frac{32}{3\sqrt{2}$}$ .

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Question

Note: Figure NOT drawn to scale.

The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

Tap to reveal answer

Answer

We are looking for the height of the pyramid.

The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows:

$B = $$\frac{s^{2}$$ $\sqrt{3}$ }{4}$

$B = $$\frac{4^{2}$$ $\sqrt{3}$ }{4}$

$B = $\frac{16 \sqrt{3}$ }{4}$

$B = 4$\sqrt{3}$$

The height of a pyramid can be calculated using the fomula

$V = $\frac{1}{3}$Bh$

We set and $B = 4$\sqrt{3}$$ and solve for :

$$\frac{1}{3}$ \cdot 4$\sqrt{3}$ \cdot h = 25$

$h = $\frac{25 \cdot 3}{4 \sqrt{3}$} = $\frac{75}{4 \sqrt{3}$} \approx $\frac{75}{4 \cdot 1.7321}$ \approx 10.8$

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Question

Note: Figure NOT drawn to scale.

Give the volume (nearest tenth) of the above triangular pyramid.

Tap to reveal answer

Answer

The height of the pyramid is . The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows:

$B = $$\frac{s^{2}$$ $\sqrt{3}$ }{4}$

$B = $$\frac{4^{2}$$ $\sqrt{3}$ }{4}$

$B = $\frac{16 \sqrt{3}$ }{4}$

$B = 4$\sqrt{3}$$

The volume of a pyramid can be calculated using the fomula

$V = $\frac{1}{3}$Bh$

$V = $\frac{1}{3}$ \cdot 4$\sqrt{3}$ \cdot 8 = $\frac{32\sqrt{3}$ }{3} \approx $\frac{32 \cdot 1.7321}{3}$ \approx 18.5$

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Knew It

How to find the volume of a tetrahedron - PSAT Math

Note: Figure NOT drawn to scale. The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

We are looking for the height of the pyramid. The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows: The height of a pyramid can be calculated using the fomula We set and and solve for :

Note: Figure NOT drawn to scale. Give the volume (nearest tenth) of the above triangular pyramid.

The height of the pyramid is . The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows: The volume of a pyramid can be calculated using the fomula

A regular tetrahedron has an edge length of . What is its volume?

The volume of a tetrahedron is found with the equation , where represents the length of an edge of the tetrahedron. Plug in 4 for the edge length and reduce as much as possible to find the answer: The volume of the tetrahedron is .

Note: Figure NOT drawn to scale. The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

We are looking for the height of the pyramid. The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows: The height of a pyramid can be calculated using the fomula We set and and solve for :

Note: Figure NOT drawn to scale. Give the volume (nearest tenth) of the above triangular pyramid.

The height of the pyramid is . The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows: The volume of a pyramid can be calculated using the fomula

A regular tetrahedron has an edge length of . What is its volume?

The volume of a tetrahedron is found with the equation , where represents the length of an edge of the tetrahedron. Plug in 4 for the edge length and reduce as much as possible to find the answer: The volume of the tetrahedron is .

Note: Figure NOT drawn to scale. The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

We are looking for the height of the pyramid. The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows: The height of a pyramid can be calculated using the fomula We set and and solve for :

Note: Figure NOT drawn to scale. Give the volume (nearest tenth) of the above triangular pyramid.

The height of the pyramid is . The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows: The volume of a pyramid can be calculated using the fomula

A regular tetrahedron has an edge length of . What is its volume?

The volume of a tetrahedron is found with the equation , where represents the length of an edge of the tetrahedron. Plug in 4 for the edge length and reduce as much as possible to find the answer: The volume of the tetrahedron is .

Note: Figure NOT drawn to scale. The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

We are looking for the height of the pyramid. The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows: The height of a pyramid can be calculated using the fomula We set and and solve for :

Note: Figure NOT drawn to scale. Give the volume (nearest tenth) of the above triangular pyramid.

The height of the pyramid is . The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows: The volume of a pyramid can be calculated using the fomula

A regular tetrahedron has an edge length of . What is its volume?

The volume of a tetrahedron is found with the equation , where represents the length of an edge of the tetrahedron. Plug in 4 for the edge length and reduce as much as possible to find the answer: The volume of the tetrahedron is .

Note: Figure NOT drawn to scale. The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

We are looking for the height of the pyramid. The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows: The height of a pyramid can be calculated using the fomula We set and and solve for :

Note: Figure NOT drawn to scale. Give the volume (nearest tenth) of the above triangular pyramid.

The height of the pyramid is . The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows: The volume of a pyramid can be calculated using the fomula

A regular tetrahedron has an edge length of . What is its volume?

The volume of a tetrahedron is found with the equation , where represents the length of an edge of the tetrahedron. Plug in 4 for the edge length and reduce as much as possible to find the answer: The volume of the tetrahedron is .

Note: Figure NOT drawn to scale. The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

We are looking for the height of the pyramid. The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows: The height of a pyramid can be calculated using the fomula We set and and solve for :

Note: Figure NOT drawn to scale. Give the volume (nearest tenth) of the above triangular pyramid.

The height of the pyramid is . The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows: The volume of a pyramid can be calculated using the fomula

A regular tetrahedron has an edge length of . What is its volume?

The volume of a tetrahedron is found with the equation , where represents the length of an edge of the tetrahedron. Plug in 4 for the edge length and reduce as much as possible to find the answer: The volume of the tetrahedron is .

Note: Figure NOT drawn to scale. The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

We are looking for the height of the pyramid. The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows: The height of a pyramid can be calculated using the fomula We set and and solve for :

Note: Figure NOT drawn to scale. Give the volume (nearest tenth) of the above triangular pyramid.

The height of the pyramid is . The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows: The volume of a pyramid can be calculated using the fomula

Note: Figure NOT drawn to scale.

The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

Note: Figure NOT drawn to scale.

Give the volume (nearest tenth) of the above triangular pyramid.

Note: Figure NOT drawn to scale.

The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

Note: Figure NOT drawn to scale.

Give the volume (nearest tenth) of the above triangular pyramid.

Note: Figure NOT drawn to scale.

The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

Note: Figure NOT drawn to scale.

Give the volume (nearest tenth) of the above triangular pyramid.

Note: Figure NOT drawn to scale.

The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

Note: Figure NOT drawn to scale.

Give the volume (nearest tenth) of the above triangular pyramid.

Note: Figure NOT drawn to scale.

The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

Note: Figure NOT drawn to scale.

Give the volume (nearest tenth) of the above triangular pyramid.

Note: Figure NOT drawn to scale.

The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

Note: Figure NOT drawn to scale.

Give the volume (nearest tenth) of the above triangular pyramid.

Note: Figure NOT drawn to scale.

The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

Note: Figure NOT drawn to scale.

Give the volume (nearest tenth) of the above triangular pyramid.