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Intermediate Geometry : How to find the radius of a sphere

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Example Questions

Example Question #71 : Spheres

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:

$4.48\ ft$

$6.12\ ft$

$8.96\ ft$

$3.06\ ft$

$32.25\ ft$

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^rd 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

D= 6.12 ft

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

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

Possible Answers:

$2.2\:ft$

$2.4\:ft$

$4.8\:ft$

$2.3\:ft$

$2.1\:ft$

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:

$2.6\:in$

$2.64\:in$

$2.7\:in$

$2.3\:in$

$2.5\:in$

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. 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.

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

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

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

$r = 2.63\: in$

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Example Question #2 : 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:

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

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

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

$\sqrt{\pi}\:units$

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

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:

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

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

$1\:cm$

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

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

Correct answer:

$1\:cm$

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:

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

1=r^3

r=1

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Example Question #2 : 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:

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

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

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

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

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

Correct answer:

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

Explanation:

The formula for the volume of a sphere is:

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

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

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

$3=\pi r^3$

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

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

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Example Question #3 : 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:

$2\:cm$

$\sqrt{2}\:cm$

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

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

$2\sqrt 2\:cm$

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 for to find the radius:

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

2=r^2

$r=\sqrt2\:cm$

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

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

Possible Answers:

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

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

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

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

$\sqrt2\:in$

Correct answer:

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

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:

$8=4\pi r^2$

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

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

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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 #71 : Spheres

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

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

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

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

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

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

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

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