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Intermediate Geometry : How to find the radius of a sphere

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Example Questions

Example Question #1 :How To Find The Radius Of A Sphere

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

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

Possible Answers:

$6.12\ ft$

$4.48\ ft$

$3.06\ ft$

$32.25\ ft$

$8.96\ ft$

Correct answer:

$6.12\ ft$

Explanation:

The correct answer is 6.12 ft.

Plug the value of V=120 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 3^rdroot 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

D= 6.12 ft

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Example Question #2 :How To Find The Radius Of A Sphere

The volume of a sphere is $57\:ft^3$ . What is its radius?

Possible Answers:

$4.8\:ft$

$2.1\:ft$

$2.2\:ft$

$2.3\:ft$

$2.4\:ft$

Correct answer:

$2.4\:ft$

Explanation:

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

The only given information in the problem is the sphere's final volume. If the volume is $57\:ft^3$ , the formula for volume can be used to calculate the sphere's radius.

In this case,, the radius, is the only unknown variable that needs to be solved for.

$\frac{4}{3} \pi r^3 = 57$

$\frac{3}{4}\cdot \frac{1}{\pi}\cdot\frac{4}{3} \pi r^3 = 57 \cdot\frac{3}{4}\cdot \frac{1}{\pi}$

$r^3 = \frac{171}{4\cdot \pi}$

$\sqrt[3]{r^3}=\sqrt[3]{\frac{171}{4\cdot \pi}} = \sqrt[3]{13.608}$

$r=\sqrt[3]{13.608}$

r={2.387 ft}

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Example Question #3 :How To Find The Radius Of A Sphere

The area of a sphere is $87\:in^2$ . What is its radius?

Possible Answers:

$2.64\:in$

$2.5\:in$

$2.7\:in$

$2.6\:in$

$2.3\:in$

Correct answer:

$2.6\:in$

Explanation:

The only information given is the area of $87\:in^2$ .

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. Afteris substituted in for the area, the goal is to solve forby getting it by itself on one side of the equals sign.

$87=4 \cdot \pi \cdot r^2$

$\frac{87}{4\cdot\pi}=\frac{4 \cdot \pi \cdot r^2}{4\cdot\pi}$

$\sqrt{\frac{87}{4 \cdot \pi}} = \sqrt{r^2} = r$

$r = 2.63\: in$

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Example Question #1 :How To Find The Radius Of A Sphere

If the volume of a sphere is $1\:unit$ , what is the sphere's exact radius?

Possible Answers:

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

$\sqrt{\pi}\:units$

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

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

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

Correct answer:

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

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:

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

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Example Question #5 :How To Find The Radius Of A Sphere

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

Possible Answers:

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

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

$1\:cm$

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

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

Correct answer:

$1\:cm$

Explanation:

The equation for the volume of a sphere is:

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

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

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

1=r^3

r=1

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Example Question #6 :How To Find The Radius Of A Sphere

If the volume of a sphere is $4\:m^3$ , what is the radius of the sphere?

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

The formula for the volume of a sphere is:

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

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

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

$3=\pi r^3$

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

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

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Example Question #7 :How To Find The Radius Of A Sphere

Find the radius of a sphere if the surface area is $8\pi\:cm^2$ .

Possible Answers:

$2\sqrt 2\:cm$

$\sqrt{2}\:cm$

$2\:cm$

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

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

Correct answer:

$\sqrt{2}\:cm$

Explanation:

The formula for the surface area of a sphere is:

$SA=4\pi r^2$

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

$8\pi=4\pi r^2$

2=r^2

$r=\sqrt2\:cm$

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Example Question #8 :How To Find The Radius Of A Sphere

Find the radius of a sphere if its surface area is $8\:in^2$ .

Possible Answers:

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

$\sqrt2\:in$

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

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

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

Correct answer:

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

Explanation:

The surface area formula for a sphere is:

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

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

$8=4\pi r^2$

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

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

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Intermediate Geometry : How to find the radius of a sphere

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1 :How To Find The Radius Of A Sphere

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Example Question #1 :How To Find The Radius Of A Sphere

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