ACT Math - How to find the volume of a sphere

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.

What is the volume of a sphere with a diameter of $\textup{6 inches}$ (reduce all fractions)?

$\frac{108}{3}\pi\textup{ in}^3$

$36\pi\textup{ in}^3$

$108\pi\textup{ in}^3$

$\frac{864}{3}\pi\textup{ in}^3$

$144\pi\textup{ in}^3$

Explanation

The formula for the volume of a sphere is:
$v = \frac{4}{3}\pi * r^3$ , thus we need to just determine the radius and plug it into the equation. Remember that and so

And plugging in we get $\frac{108}{3}\pi \textup{in}^3$

Find the volume of a sphere whose diameter is .

$\frac{32}{3}\pi$

$\frac{256}{3}\pi$

$256\pi$

$\frac{64}{3}\pi$

$64\pi$

Explanation

To solve, simply use the formula for the volume of a sphere. Thus,

$V=\frac{4}{3}\pi{r^3}=\frac{4}{3}*\pi*2^3=\frac{4}{3}*8*\pi=\frac{32}{3}\pi$

The specifications of an official NBA basketball are that it must be 29.5 inches in circumference and weigh 22 ounces. What is the approximate volume of the basketball? Remember that the volume of a sphere is calculated by V=(4πr3)/3

92.48 cu.in.

138.43 cu.in.

434.19 cu.in.

3468.05 cu.in.

8557.46 cu.in.

Explanation

To find your answer, we would use the formula: C=2πr. We are given that C = 29.5. Thus we can plug in to get \[29.5\]=2πr and then multiply 2π to get 29.5=(6.28)r. Lastly, we divide both sides by 6.28 to get 4.70=r. Then we would plug into the formula for volume V=(4π〖(4.7)〗3) / 3 (The information given of 22 ounces is useless)

If Ariana’s orange has twice the radius of Autumn’s orange, the volume of Ariana’s orange is how many times larger than the volume of Autumn’s orange?

Explanation

Define the radius of Autumn’s orange as r. The volume of her orange is $\pi r^3$ . Ariana’s orange has twice the radius of Autumn’s, so the radius of her orange is , and the volume is $\pi(2r)^3 = 8\pi r^3$ , which is 8 times larger than Autumn’s orange.

What is the volume of a sphere with a surface area of $576\pi\textup{ ft}^2$ ? (Simplify all fractions in your answer.)

$2304\pi\textup{ ft}^3$

$18432\pi\textup{ ft}^3$

$288\pi\textup{ ft}^3$

$2304 \pi\textup{ ft}^3$

$2304 \pi\textup{ ft}^2$

Explanation

First find the radius from the surface area set the given surface area equal to the surface area formula and solve for the radius.
$576\pi = 4\pi r^2$

$144\pi = \pi r^2 ewline 144 = r^2 ewline 12 = r$

Now plug the radius into the volume formula:
$V = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi 12^3 = 2304 \pi\textup{ ft}^3$

A cube has a side dimension of 4. A sphere has a radius of 3. What is the volume of the two combined, if the cube is balanced on top of the sphere?

$64 + 36\pi$

$16 + 36\pi$

$64 + 6\pi$

$16 + 6\pi$

$4 + 36\pi$

Explanation

$V_{cube}=(\text{side})^3=(4)^3=64$

$V{sphere}=\frac{4}{3}\pi r^3=\frac{4}{3}\pi(3^3)=\frac{4}{3}\pi(27)=36\pi$

$V_{total}=64+36\pi$

If the diameter of a sphere is , find the approximate volume of the sphere?

$167\pi$

$205\pi$

$95\pi$

$143\pi$

$334\pi$

Explanation

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

Radius is $\frac{1}{2}$ of the diameter so the radius = 5.

$V=\frac{4}{3}\pi5^{3}$

or $V=\frac{500}{3\pi}$

which is approximately $167\pi$

For a sphere the volume is given by V = (4/3)πr_3 and the surface area is given by A = 4_πr_2. If the sphere has a surface area of 256_π, what is the volume?

683_π_

615_π_

300_π_

750_π_