How to find the volume of a sphere in pre-algebra

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Math › How to find the volume of a sphere in pre-algebra

Questions 1 - 10

1

What is the volume of a sphere with a radius of ?

$36\pi$

$\frac{4}{3}\pi$

$9\pi$

$27\pi$

$81\pi$

Explanation

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

Plug in our radius to solve:

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

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

$V=\frac{4}{3}*\pi*27$

$V=36\pi$

2

What is the volume of a sphere with a radius of ?

$972 \pi$

$729\pi$

$693\pi$

$1272\pi$

Explanation

To solve for the volume of a sphere, use the equation:

$Volume=\frac{4}{3}(\pi)(radius^{3})$

Substitute the given radius into the equation:

$Volume=\frac{4}{3}(\pi)(9^{3})$

$Volume=(\frac{4}{3})(\pi)(729)$

$Volume=972 \pi$

3

What is the volume of a sphere with a radius of ?

$V=36\pi$

$V=27\pi$

$V=9\pi$

$V=45\pi$

Explanation

To solve for the volume of a sphere you must first know the equation for the volume of a sphere.

The equation is

Then plug the radius into the equation for yielding

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

Then cube the radius to get

$V=\frac{4}{3}(27})(\pi)$

Multiply the answer by and to yield

$V=36\pi$ .

The answer is $V=36\pi$ .

4

What is the volume of a sphere with a radius of ?

$7776\pi$

$4800\pi$

$6453\pi$

$8000\pi$

Explanation

To solve for the volume of a sphere you must first know the equation for the volume of a sphere.

The equation is

Then plug the radius into the equation for yielding

$V=(\frac{4}{3})(18^{3})(\pi)$

Then cube the radius to get

$V=(\frac{4}{3})(5832)(\pi)$

Multiply the answer by and to yield $V=7776\pi$ .

The answer is $7776\pi$ .

5

What is the volume of a sphere with a radius of ?

$457.33\pi$

$49\pi$

$571.55\pi$

$343\pi$

Explanation

To solve for the volume of a sphere you must first know the equation for the volume of a sphere.

The equation is

Then plug the radius into the equation for yielding $V=\frac{4}{3}\pi(7^{3})$

Then cube the radius to get $V=\frac{4}{3}\pi(343)$

Multiply the answer by $\frac{4}{3}$ and to yield $457.33\pi$ .

The answer is $457.33\pi$ .

6

What is the volume of a sphere with a radius of ?

$166\tfrac{2}{3}\pi$

$500\pi$

$125\pi$

$375\pi$

$84\tfrac{1}{3}\pi$

Explanation

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

Plug in our radius to solve:

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

$V=\frac{4}{3}\pi *5^3$

$V=\frac{4}{3}*\pi*125$

$V=166\tfrac{2}{3}\pi$

7

What is the volume of a sphere with a radius of ?

$36\pi$

$12\pi$

$27\pi$

$6\pi$

$108\pi$

Explanation

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

Plug in our given values.

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

$V=\frac{4}{3}\pi*27$

$V=36\pi$

8

What is the volume of a sphere with a radius of ?

$10\tfrac{2}{3}\pi$

$6\pi$

$21\tfrac{1}{3}\pi$

$8\pi$

$64\pi$

Explanation

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

Plug in our radius to solve:

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

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

$V=\frac{4}{3}*\pi*8$

$V=10\tfrac{2}{3}\pi$

9

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

$\frac{4}{3}\pi^4$

Undefined

$\frac{4}{3} \pi^3$

$\frac{4}{3}\pi$

$\frac{\pi}{4}$

Explanation

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

Plug in our radius to solve:

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

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

Remember, an exponent just means a number times itself. That means that $\pi*\pi^3=\pi^4$ .

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

10

If the volume of a sphere is $300\pi$ , what is the radius?

$6.08\pi$

Explanation

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

Plug in our given information.

$300\pi=\frac{4}{3}\pi r^3$

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

$300=\frac{4}{3}r^3$

Divide both sides by $\frac{4}{3}$ . Since we're dividing by a fraction, that means we need to multiply both sides by the reciprocal: $\frac{3}{4}$ .

$300*\frac{3}{4}=r^3$

$\sqrt[3]{225}=\sqrt[3]{r^3}$

$\sqrt[3]{225}=r$

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