How to find the radius of a sphere

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Math › How to find the radius of a sphere

Questions 1 - 10

If the volume of a sphere is $120\ ft^{3}$ , what is the approximate length of its diameter?

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

$6.12\ ft$

$4.48\ ft$

$3.06\ ft$

$8.96\ ft$

$32.25\ ft$

Explanation

The correct answer is 6.12 ft.

Plug the value of into the equation so that

$120=\frac{4}{3}\pi r^{3}$

Multiply both sides by 3 to get

$360=4\pi r^{3}$

Then divide both sides by $4\pi$ to get

$28.65=r^{3}$

Then take the 3rd root of both sides to get 3.06 ft for the radius. Finally, you have to multiply by 2 on both sides to get the diameter. Thus

What is the radius of a sphere with a volume of $288\pi$ ?

Explanation

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

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

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

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

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

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

What is the radius of a sphere that has a surface area of $16\pi$ ?

$2\sqrt{\pi }$

$8\pi$

$8\sqrt{\pi }$

$\sqrt{2\pi }$

Explanation

The standard equation to find the area of a sphere is $SA=4\pi r^2$ where denotes the radius. Rearrange this equation in terms of :

$r=\sqrt{\frac{SA}{4\pi }}$

To find the answer, substitute the given surface area into this equation and solve for the radius:

$r=\sqrt{\frac{16\pi }{4\pi }}=\sqrt{4}=2$

Given that the volume of a sphere is $12\pi$ , what is the radius?

$\sqrt[3]{9}$

$\sqrt{9\pi }$

$9\pi$

$\sqrt[3]{12 }$

Explanation

The standard equation to find the volume of a sphere is

$V=\frac{4}{3}\pi r^3$ where denotes the radius. Rearrange this equation in terms of :

$r=\sqrt[3]{\frac{3V}{4\pi }}$

Substitute the given volume into this equation and solve for the radius:

$r=\sqrt[3]{\frac{3V}{4\pi }}=\sqrt[3]{\frac{3\cdot 12\pi }{4\pi }}=\sqrt[3]{\frac{36\pi }{4\pi }}=\sqrt[3]{9 }$

Given the volume of a sphere is $\frac{4}{3}\pi:cm^3$ , what is the radius?

$\frac{4}{3}:cm$

$\frac{\sqrt2}{3}:cm$

$\frac{1}{2}:cm$

$\frac{1}{4}:cm$

Explanation

The equation for the volume of a sphere is:

$V=\frac{4}{3}\pi r^3$ , where is the length of the sphere's radius.

Plug in the given volume and solve for to calculate the sphere's radius:

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

If the volume of a sphere is , what is the sphere's exact radius?

$\sqrt[3]{\frac{3}{4\pi}}:units$

$\sqrt[3]{\frac{4\pi}{3}}:units$

$\sqrt{\frac{1}{\pi}}:units$

$\sqrt{\pi}:units$

$\sqrt{\frac{2}{3\pi}}:units$

Explanation

Write the formula for the volume of a sphere:

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

Plug in the given volume and solve for the radius, .

$1=\frac{4}{3}\pi r^3$

Start by multiplying each side of the equation by $\frac{3}{4}$ :

$\frac{3}{4}\cdot1=\frac{4}{3}\pi r^3\cdot\frac{3}{4}$

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

Now, divide each side of the equation by $\pi$ :

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

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

Finally, take the cubed root of each side of the equation:

$r=\sqrt[3]{\frac{3}{4\pi}}$

If the volume of a sphere is , what is the radius of the sphere?

$\sqrt[3]{\frac{3}{\pi}}:m$

$\sqrt[3]{3\pi}:m$

$\sqrt[3]{\frac{16}{3\pi}}:m$

$\sqrt[3]{\frac{3}{\pi}}:m$

$\sqrt[3]{\frac{1}{3\pi}}:m$

Explanation

The formula for the volume of a sphere is:

$V=\frac{4}{3}\pi r^3$ , where is the sphere's radius.

Plug in the volume and solve for , the sphere's radius:

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

$3=\pi r^3$

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

$r=\sqrt[3]{\frac{3}{\pi}}:m$

Find the radius of a sphere if its surface area is .

$\sqrt\frac{2}{\pi}:in$

$\sqrt2:in$

$\sqrt\frac{\pi}{2}:in$

$\sqrt\frac{8}{\pi}:in$

$\sqrt\frac{\pi}{8}:in$

Explanation

The surface area formula for a sphere is:

$A=4\pi r^2$ , where is the sphere's radius.

Substitute the given value for the sphere's area into the equation and solve for to find the radius:

$8=4\pi r^2$

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

$r=\sqrt{\frac{2}{\pi}}:in$

The area of a sphere is . What is its radius?

Explanation

The only information given is the area of .

This problem may be approached "backwards," where the area formula for a sphere can be used to solve for the radius. This is possible because the formula for area is $Area = 4 \cdot \pi \cdot r^2$ , where (the radius) is what we're looking for. After is substituted in for the area, the goal is to solve for by getting it by itself on one side of the equals sign.