Spheres

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1

The volume of a sphere is $2 8 8 \pi$ . What is the diameter?

Explanation

To find the diameter of the sphere, we need to find the radius.

The volume of a sphere is $V=\frac{4}{3}\pi r^3$ .

Plug in our given values.

$2 88\pi=\frac{4}{3}\pi r^3$

Notice that the $\pi$ 's cancel out.

$288=\frac{4}{3}r^3$

$\frac{3}{4}*288=r^3$

$\sqrt[3]{216}=\sqrt[3]{r^3}$

The diameter is twice the radius, so .

2

Find the volume of the following sphere.

Sphere

$288 \pi m^3$

$270 \pi m^3$

$300 \pi m^3$

$312 \pi m^3$

$360 \pi m^3$

Explanation

The formula for the volume of a sphere is:

$V=\frac{4}{3} \pi r^3$

where is the radius of the sphere.

Plugging in our values, we get:

$V=\frac{4}{3} \pi (6m)^3$

$V=\frac{4}{3} \pi 216m^3 = 288 \pi m^3$

3

What is the volume of a sphere with a diameter of 6 in?

$36\pi\ in^{3}$

$216\pi\ in^{3}$

$108\pi\ in^{3}$

$72\pi\ in^{3}$

$288\pi\ in^{3}$

Explanation

The formula for the volume of a sphere is:

$V=\frac{4}{3}\pi r^{3}$

where = radius. The diameter is 6 in, so the radius will be 3 in.

4

What is the surface area of a sphere with a radius of ?

$576\pi$

$144\pi$

$288\pi$

$24\pi$

Explanation

To solve for the surface area of a sphere you must remember the formula:

First, plug the radius into the equation for :

$SA=(4)(12^{2})(\pi)$

Since $(12^{2})=144$ , the surface area is $(4)(144)(\pi)=576\pi$ .

The answer is therefore $576\pi$ .

5

Find the volume of the following sphere.

Sphere

$288 \pi m^3$

$270 \pi m^3$

$300 \pi m^3$

$312 \pi m^3$

$360 \pi m^3$

Explanation

The formula for the volume of a sphere is:

$V=\frac{4}{3} \pi r^3$

where is the radius of the sphere.

Plugging in our values, we get:

$V=\frac{4}{3} \pi (6m)^3$

$V=\frac{4}{3} \pi 216m^3 = 288 \pi m^3$

6

What is the diameter of a sphere with a volume of $36\pi$ ?

Explanation

The volume of a sphere is determined by the following equation:

$V=\frac{4}{3}\pi r^3$

$36\pi=\frac{4}{3}\pi r^3$

$(\frac{3}{4})36\pi=(\frac{3}{4})(\frac{4}{3})\pi r^3$

$\frac{27\pi}{\pi}=\frac{\pi r^3}{\pi}$

$\sqrt[3]{27}=\sqrt[3]{r^3}$

7

What is the diameter of a sphere with a volume of $36\pi$ ?

Explanation

The volume of a sphere is determined by the following equation:

$V=\frac{4}{3}\pi r^3$

$36\pi=\frac{4}{3}\pi r^3$

$(\frac{3}{4})36\pi=(\frac{3}{4})(\frac{4}{3})\pi r^3$

$\frac{27\pi}{\pi}=\frac{\pi r^3}{\pi}$

$\sqrt[3]{27}=\sqrt[3]{r^3}$

8

The volume of a sphere is $2 8 8 \pi$ . What is the diameter?

Explanation

To find the diameter of the sphere, we need to find the radius.

The volume of a sphere is $V=\frac{4}{3}\pi r^3$ .

Plug in our given values.

$2 88\pi=\frac{4}{3}\pi r^3$

Notice that the $\pi$ 's cancel out.

$288=\frac{4}{3}r^3$

$\frac{3}{4}*288=r^3$

$\sqrt[3]{216}=\sqrt[3]{r^3}$

The diameter is twice the radius, so .

9

What is the volume of a sphere with a diameter of 6 in?

$36\pi\ in^{3}$

$216\pi\ in^{3}$

$108\pi\ in^{3}$

$72\pi\ in^{3}$

$288\pi\ in^{3}$

Explanation

The formula for the volume of a sphere is:

$V=\frac{4}{3}\pi r^{3}$

where = radius. The diameter is 6 in, so the radius will be 3 in.

10

What is the surface area of a sphere with a radius of ?

$576\pi$

$144\pi$

$288\pi$

$24\pi$

Explanation

To solve for the surface area of a sphere you must remember the formula:

First, plug the radius into the equation for :

$SA=(4)(12^{2})(\pi)$

Since $(12^{2})=144$ , the surface area is $(4)(144)(\pi)=576\pi$ .

The answer is therefore $576\pi$ .

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