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

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

$5625 \pi$

$50 \pi$

$25 \pi^{2}$

Explanation

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

$5625 \pi$

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

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

$\frac{2020}{169 \pi}$

$\frac{505}{169 \pi}$

$\frac{1010}{169}$

$\frac{1020100}{28561 \pi^{2}}$

Explanation

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

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

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

$\frac{2007}{143}$

$\frac{6021}{143}$

$\frac{669}{143}$

$\frac{2007 \pi}{143}$

$\frac{4028049}{20449}$

Explanation

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

$\frac{2007}{143}$

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

Round your answer to decimal places.

Explanation

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.

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

Round your answer to decimal places.

Explanation

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.

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

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

$\frac{793}{36 \pi}$

$\frac{793}{144 \pi}$

$\frac{793}{72}$

$\frac{628849}{5184 \pi^{2}}$

Explanation

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

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

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

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

$\frac{554}{3 \pi}$

$\frac{277}{6 \pi}$

$\frac{277}{3}$

$\frac{76729}{9 \pi^{2}}$

Explanation

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

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

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

Round your answer to decimal places.

Explanation

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.

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

Round your answer to decimal places.

Explanation

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 800 for and solve for .

$\800 = 6 l \l = 133.333333333333$

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 133.33333333333334 for .

$\V = \left( 133.33333333333334 \right)^{3} \V = 2370370.37037037$

So the final answer is.

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

Round your answer to decimal places.

Explanation

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.

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

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