How to find the surface area of a cylinder - ISEE Upper Level Quantitative Reasoning

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Question

If a cylinder has a height of 6 mm and a radius of 12 mm, what is its surface area?

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Answer

If a cylinder has a height of 6 mm and a radius of 12 mm, what is its surface area?

Find surface area with the following formula:

$A=2\pi r h +2\pi $r^2$$

This works because we are adding the area of the two bases to the area of the side.

Plug in and simplify:

$A=2\pi (12mm)(6mm) +2\pi $(12mm)^2$=144\pi $mm^2$+288\pi $mm^2$=432 \pi $mm^2$$

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Question

Find the volume of a cylinder with a diameter of 14cm and a height of 8cm.

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Answer

To find the volume of a cylinder, we will use the following formula:

$V = \pi $r^2$ h$

where r is the radius and h is the height of the cylinder.

Now, we know the diameter of the cylinder is 14cm. We also know that the diameter is two times the radius. Therefore, the radius is 7cm.

We know the height of the cylinder is 8cm.

Knowing all of this, we can substitute into the formula. We get

$V = \pi \cdot $(7$\text{cm}$)^2$ \cdot 8$\text{cm}$$

$V = \pi \cdot $49$\text{cm}$^2$ \cdot 8$\text{cm}$$

$V = \pi \cdot $392$\text{cm}$^3$$

$V = 392\pi $\text{ $cm}$^3$$

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Question

If a cylinder has a height of 6 mm and a radius of 12 mm, what is its surface area?

Tap to reveal answer

Answer

If a cylinder has a height of 6 mm and a radius of 12 mm, what is its surface area?

Find surface area with the following formula:

$A=2\pi r h +2\pi $r^2$$

This works because we are adding the area of the two bases to the area of the side.

Plug in and simplify:

$A=2\pi (12mm)(6mm) +2\pi $(12mm)^2$=144\pi $mm^2$+288\pi $mm^2$=432 \pi $mm^2$$

← Didn't Know|Knew It →

Question

Find the volume of a cylinder with a diameter of 14cm and a height of 8cm.

Tap to reveal answer

Answer

To find the volume of a cylinder, we will use the following formula:

$V = \pi $r^2$ h$

where r is the radius and h is the height of the cylinder.

Now, we know the diameter of the cylinder is 14cm. We also know that the diameter is two times the radius. Therefore, the radius is 7cm.

We know the height of the cylinder is 8cm.

Knowing all of this, we can substitute into the formula. We get

$V = \pi \cdot $(7$\text{cm}$)^2$ \cdot 8$\text{cm}$$

$V = \pi \cdot $49$\text{cm}$^2$ \cdot 8$\text{cm}$$

$V = \pi \cdot $392$\text{cm}$^3$$

$V = 392\pi $\text{ $cm}$^3$$

← Didn't Know|Knew It →

Question

If a cylinder has a height of 6 mm and a radius of 12 mm, what is its surface area?

Tap to reveal answer

Answer

If a cylinder has a height of 6 mm and a radius of 12 mm, what is its surface area?

Find surface area with the following formula:

$A=2\pi r h +2\pi $r^2$$

This works because we are adding the area of the two bases to the area of the side.

Plug in and simplify:

$A=2\pi (12mm)(6mm) +2\pi $(12mm)^2$=144\pi $mm^2$+288\pi $mm^2$=432 \pi $mm^2$$

← Didn't Know|Knew It →

Question

Find the volume of a cylinder with a diameter of 14cm and a height of 8cm.

Tap to reveal answer

Answer

To find the volume of a cylinder, we will use the following formula:

$V = \pi $r^2$ h$

where r is the radius and h is the height of the cylinder.

Now, we know the diameter of the cylinder is 14cm. We also know that the diameter is two times the radius. Therefore, the radius is 7cm.

We know the height of the cylinder is 8cm.

Knowing all of this, we can substitute into the formula. We get

$V = \pi \cdot $(7$\text{cm}$)^2$ \cdot 8$\text{cm}$$

$V = \pi \cdot $49$\text{cm}$^2$ \cdot 8$\text{cm}$$

$V = \pi \cdot $392$\text{cm}$^3$$

$V = 392\pi $\text{ $cm}$^3$$

← Didn't Know|Knew It →

Question

If a cylinder has a height of 6 mm and a radius of 12 mm, what is its surface area?

Tap to reveal answer

Answer

If a cylinder has a height of 6 mm and a radius of 12 mm, what is its surface area?

Find surface area with the following formula:

$A=2\pi r h +2\pi $r^2$$

This works because we are adding the area of the two bases to the area of the side.

Plug in and simplify:

$A=2\pi (12mm)(6mm) +2\pi $(12mm)^2$=144\pi $mm^2$+288\pi $mm^2$=432 \pi $mm^2$$

← Didn't Know|Knew It →

Question

Find the volume of a cylinder with a diameter of 14cm and a height of 8cm.

Tap to reveal answer

Answer

To find the volume of a cylinder, we will use the following formula:

$V = \pi $r^2$ h$

where r is the radius and h is the height of the cylinder.

Now, we know the diameter of the cylinder is 14cm. We also know that the diameter is two times the radius. Therefore, the radius is 7cm.

We know the height of the cylinder is 8cm.

Knowing all of this, we can substitute into the formula. We get

$V = \pi \cdot $(7$\text{cm}$)^2$ \cdot 8$\text{cm}$$

$V = \pi \cdot $49$\text{cm}$^2$ \cdot 8$\text{cm}$$

$V = \pi \cdot $392$\text{cm}$^3$$

$V = 392\pi $\text{ $cm}$^3$$

← Didn't Know|Knew It →

Knew It

How to find the surface area of a cylinder - ISEE Upper Level Quantitative Reasoning

If a cylinder has a height of 6 mm and a radius of 12 mm, what is its surface area?

If a cylinder has a height of 6 mm and a radius of 12 mm, what is its surface area? Find surface area with the following formula: This works because we are adding the area of the two bases to the area of the side. Plug in and simplify:

Find the volume of a cylinder with a diameter of 14cm and a height of 8cm.

If a cylinder has a height of 6 mm and a radius of 12 mm, what is its surface area?

If a cylinder has a height of 6 mm and a radius of 12 mm, what is its surface area? Find surface area with the following formula: This works because we are adding the area of the two bases to the area of the side. Plug in and simplify:

Find the volume of a cylinder with a diameter of 14cm and a height of 8cm.

If a cylinder has a height of 6 mm and a radius of 12 mm, what is its surface area?

If a cylinder has a height of 6 mm and a radius of 12 mm, what is its surface area? Find surface area with the following formula: This works because we are adding the area of the two bases to the area of the side. Plug in and simplify:

Find the volume of a cylinder with a diameter of 14cm and a height of 8cm.

If a cylinder has a height of 6 mm and a radius of 12 mm, what is its surface area?

If a cylinder has a height of 6 mm and a radius of 12 mm, what is its surface area? Find surface area with the following formula: This works because we are adding the area of the two bases to the area of the side. Plug in and simplify:

Find the volume of a cylinder with a diameter of 14cm and a height of 8cm.