Circumference and Area of a Circle, Volume of a Cylinder, Pyramid, and Cone Formulas: CCSS.Math.Content.HSG-GMD.A.1 - Geometry

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Question

If a cylinder has a volume of and a radius of what is the height?

Answer

In order to find the height, we need to recall the equation for the volume of a cylinder.

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

Since we are given the volume, and the radius, we can simply plug in those values into the equation.

$\V=1010 \r=13$

$\1010 = 169 \pi h \\h = \frac{1010}{169 \pi}$

Thus the height is

$\frac{1010}{169 \pi}$

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Question

If a cone has a radius of and a height of what is the volume?

Answer

In order to find the volume, we need to recall the equation for the volume of a cone.

$V = \frac{\pi h}{3} r^{2}$

Since we are given the radius, and the height, we can simply plug in those values into the equation.

$\r=8 \h=11$

$V = \frac{704 \pi}{3}$
Thus the volume is

$\frac{704 \pi}{3}$

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Question

If a cone has a volume of and a radius of what is the height?

Answer

In order to find the height, we need to recall the equation for the volume of a cone.

$V = \frac{\pi h}{3} r^{2}$
Since we are given the volume, and the radius, we can simply plug in those values into the equation.

$\V=277 \r=3$

$\277 = 3 \pi h \\h = \frac{277}{3 \pi}$

Thus the height is

$\frac{277}{3 \pi}$

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Question

If a pyramid has a base width of a base length of and a volume of what is the height?

Answer

In order to find the height, we need to recall the equation for the volume of a pyramid,

$V = \frac{h lw}{3}$

Since we are given the length, width, and volume, we can simply plug those values into the equation.

$669 = \frac{143 h}{3}$

Now we solve for .

$h = \frac{2007}{143}$

Thus the height is

$\frac{2007}{143}$

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Question

If a cylinder has a volume of and a radius of what is the height?

Answer

In order to find the height, we need to recall the equation for the volume of a cylinder.

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

Since we are given the volume, and the radius, we can simply plug in those values into the equation.

$\V=837 \r=2$

$837 = 4 \pi h = \frac{837}{4 \pi}$

Thus the height is

$\frac{837}{4 \pi}$

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Question

If a cylinder has a volume of and a radius of what is the height?

Answer

In order to find the height, we need to recall the equation for the volume of a cylinder.

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

Since we are given the volume, and the radius, we can simply plug in those values into the equation.

$\V=909 \r=10$

$\909 = 100 \pi h \\h = \frac{909}{100 \pi}$

Thus the height is

$\frac{909}{100 \pi}$

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Question

If a cylinder has a volume of and a radius of what is the height?

Answer

In order to find the height, we need to recall the equation for the volume of a cylinder.

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

Since we are given the volume, and the radius, we can simply plug in those values into the equation.

$\1586 = 144 \pi h \\h = \frac{793}{72 \pi}$

Thus the height is

$\frac{793}{72 \pi}$

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Question

If a cone has a volume of and a radius of what is the height?

Answer

In order to find the height, we need to recall the equation for the volume of a cone.

$V = \frac{\pi h}{3} r^{2}$

Since we are given the volume, and the radius, we can simply plug in those values into the equation.

$\ 1928 = 3 \pi h \\h = \frac{1928}{3 \pi}$

Thus the height is

$\frac{1928}{3 \pi}$

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Question

If a circle has a circumference of what is the radius?

Answer

In order to find the radius of a circle, we need to recall the equation that involves both the radius and circumference.

$C = 2 \pi r$

Since we are given the circumference, we simply substitute 33 for $\uptext{C}$ , and solve for $\uptext{r}$ .

$33 = 2 \pi r$

Divide by $2 \pi$ on each side to get

$r = \frac{33}{2 \pi}$

Thus the radius is

$\frac{33}{2 \pi}$

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Question

If a cylinder has a radius of and a height of what is the volume?

Answer

In order to find the volume, we need to recall the equation for the volume of a cylinder.

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

Since we are given the radius, and the height, we can simply plug in those values into the equation.

$\r=15\rightarrow r^2=225 \h=25$

$V = 5625 \pi$

Thus the volume is

$5625 \pi$

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Question

If a cylinder has a radius of and a height of what is the volume?

Answer

In order to find the volume, we need to recall the equation for the volume of a cylinder.

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

Since we are given the radius, and the height, we can simply plug in those values into the equation.

$\r=11\rightarrow r^2=121 \h=4$

$V = 484 \pi$

Thus the volume is

$484 \pi$

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Question

If a cylinder has a radius of and a height of what is the volume?

Answer

In order to find the volume, we need to recall the equation for the volume of a cylinder.

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

Since we are given the radius, and the height, we can simply plug in those values into the equation.

$\r=2\rightarrow r^2=4 \h=22$

$V = 88 \pi$

Thus the volume is

$88 \pi$

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Question

Find the volume of a cube, if its surface area is .

Round your answer to decimal places.

Answer

In order to find the volume, we need to remember the equation that involves both surface area, and volume.

Where is surface area and l is the length.

Now we plug 539 for and solve for .

$\539 = 6 l \l = 89.8333333333333$

Now since we have the width, we can plug it into the volume formula, which is

$V = w^{3}$

Where w is the width and V volume.

Now plug in for .

$\V = \left( 89.83333333333333 \right)^{3} \V = 724957.49537037$

So the final answer is.

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Question

Find the volume of a cube, if its surface area is .

Round your answer to decimal places.

Answer

In order to find the volume, we need to remember the equation that involves both surface area, and volume.

Where is surface area and is the length.

Now we plug 715 for and solve for .

$\715 = 6 l \l = 119.166666666667$

Now since we have the width, we can plug it into the volume formula, which is

$V = w^{3}$

Where is the width and volume.

Now plug in 119.16666666666667 for .

$\V = \left( 119.16666666666667 \right)^{3} \V = 1692249.4212963$

So the final answer is.

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Question

Find the volume of a cube, if its surface area is .

Round your answer to decimal places.

Answer

In order to find the volume, we need to remember the equation that involves both surface area, and volume.

Where is surface area and is the length.

Now we plug 729 for and solve for .

$\729 = 6 l \l = 121.5$

Now since we have the width, we can plug it into the volume formula, which is

$V = w^{3}$

Where is the width and volume.

Now plug in 121.5 for .

$\V = \left( 121.5 \right)^{3} \V = 1793613.375$

So the final answer is.

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Question

Find the volume of a cube, if its surface area is .

Round your answer to decimal places.

Answer

In order to find the volume, we need to remember the equation that involves both surface area, and volume.

Where is surface area and is the length.

Now we plug 925 for and solve for .

$\925 = 6 l \l = 154.166666666667$

Now since we have the width, we can plug it into the volume formula, which is

$V = w^{3}$

Where w is the width and volume.

Now plug in 154.16666666666666 for .

$\V = \left( 154.16666666666666 \right)^{3} \V = 3664134.83796296$

So the final answer is.

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Question

Find the volume of a cube, if its surface area is .

Round your answer to decimal places.

Answer

In order to find the volume, we need to remember the equation that involves both surface area, and volume.

Where is surface area and is the length.

Now we plug 584 for and solve for .

$\584 = 6 l \l = 97.3333333333333$

Now since we have the width, we can plug it into the volume formula, which is

$V = w^{3}$

Where is the width and volume.

Now plug in 97.33333333333333 for .

$\V = \left( 97.33333333333333 \right)^{3} \V = 922114.37037037$

So the final answer is.

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Question

Find the volume of a cube, if its surface area is .

Round your answer to decimal places.

Answer

In order to find the volume, we need to remember the equation that involves both surface area, and volume.

Where is surface area and is the length.

Now we plug 744 for and solve for .

$\744 = 6 l \l = 124.0$

Now since we have the width, we can plug it into the volume formula, which is

$V = w^{3}$

Where is the width and volume.

Now plug in 124.0 for .

$\V = \left( 124.0 \right)^{3} \V = 1906624.0$

So the final answer is.

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Question

Find the volume of a cube, if its surface area is .

Round your answer to decimal places.

Answer

In order to find the volume, we need to remember the equation that involves both surface area, and volume.

Where is surface area and is the length.

Now we plug 511 for and solve for .

$\511 = 6 l \l = 85.1666666666667$

Now since we have the width, we can plug it into the volume formula, which is

$V = w^{3}$

Where w is the width and V volume.

Now plug in 85.16666666666667 for .

$\V = \left( 85.16666666666667 \right)^{3} \V = 617744.587962963$

So the final answer is.

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Question

Find the volume of a cube, if its surface area is .

Round your answer to decimal places.

Answer

In order to find the volume, we need to remember the equation that involves both surface area, and volume.

Where is surface area and is the length.

Now we plug 520 for and solve for .

$\520 = 6 l \l = 86.6666666666667$

Now since we have the width, we can plug it into the volume formula, which is

$V = w^{3}$

Where is the width and volume.

Now plug in 86.66666666666667 for .

$\V = \left( 86.66666666666667 \right)^{3} \V = 650962.962962963$

So the final answer is.

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