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Intermediate Geometry : How to find the diameter of a sphere

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

The surface area of a sphere is $100\pi \; in^{2}$ . What is the diameter of the sphere?

Possible Answers:

$10\; in$

$20\; in$

$5\; in$

$15\; in$

Correct answer:

$10\; in$

Explanation:

The surface area of a sphere is given by $SA=4\pi r^{2}$

So the equation to sovle becomes $4\pi r^{2}=100\pi$ or $r^{2}=25$ so $r=5\; in$

To answer the question we need to find the diameter:

$d=2r=2\cdot 5=10\; in$

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

If the volume of a sphere is $2\:units$ , what is the sphere's diameter?

Possible Answers:

$2\sqrt[3]{\frac{2\pi}{3}}$

$2\sqrt[3]{\frac{3}{2\pi}}$

$\sqrt[3]{\frac{2\pi}{3}}$

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

$\sqrt[3]{\frac{3}{2\pi}}$

Correct answer:

$2\sqrt[3]{\frac{3}{2\pi}}$

Explanation:

Write the formula for the volume of a sphere:

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

Plug in the volume and find the radius by solving for :

$2=\frac{4}{3}\pi r^3$

Start solving for by multiplying both sides of the equation by :

$2\cdot3=\frac{4}{3}\pi r^3\cdot3$

$6=4\pi r^3$

Now, divide each side of the equation by $4\pi$ :

$\frac{6}{4\pi}=\frac{4\pi r^3}{4\pi}$

$\frac{6}{4\pi}=r^3$

Reduce the left side of the equation:

$\frac{3}{2\pi}=r^3$

Finally, take the cubed root of both sides of the equation:

$\sqrt[3]{\frac{3}{2\pi}}=r$

Keep in mind that you've solved for the radius, not the diameter. The diameter is double the radius, which is: $2\sqrt[3]{\frac{3}{2\pi}}$ .

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

The circumference of a sphere is $84.823 \:in$ . Find the radius.

Possible Answers:

$27.0\:in$

$14.0\: in$

$13.5\:in$

$27.5\:in$

$13.7\:in$

Correct answer:

$13.5\:in$

Explanation:

If the circumference of a sphere is $84.823 \:in$ , that means we can easily solve for the diameter by using $C=\pi \cdot d$ . This is the equation to find the circumference.

By substituting in the value for circumference (), we can solve for the missing variable :

$84.823\:in= \pi \cdot d$

$\frac{84.823\:in}{ \pi}= d$

$d = 27\: in$

To find the radius of the sphere, we need to divide this value by :

$r=\frac{d}{2}=\frac{27\:in}{2}=13.5\:in$

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Example Question #4 : How To Find The Diameter Of A Sphere

Find the diameter of a sphere if the volume is $\pi$ .

Possible Answers:

$2\sqrt[3]{\frac{3}{4}}$

$\frac{1}{2}$

$\sqrt[3]{\frac{3}{4}}$

Correct answer:

$2\sqrt[3]{\frac{3}{4}}$

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.

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

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

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

The diameter is double the radius.

$d=2\sqrt[3]{\frac{3}{4}}$

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

Find the diameter of a sphere if the volume is $\pi^2$ .

Possible Answers:

$2\sqrt[3]{\frac{3}{4\pi}}$

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

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

$2\sqrt\pi$

$2\sqrt[3]{\frac{3\pi}{4}}$

Correct answer:

$2\sqrt[3]{\frac{3\pi}{4}}$

Explanation:

Write the volume for the sphere.

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

Substitute the volume and solve for the radius.

$\pi^2=\frac{4}{3}\pi r^3$

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

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

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

Double the radius to find diameter.

$d=2\sqrt[3]{\frac{3}{4}\pi}$

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

Find the diameter of a sphere with the volume listed below.

$V=288\pi$

Possible Answers:

Correct answer:

Explanation:

In order to solve, we must the given volume into the volume formula for a sphere.

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

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

Divide both sides by pi.

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

Multiply both sides by 3.

$216 =(r^{3})$

Take the cube root of both sides to find the radius.

r=6

Double the radius to get the diameter, diameter is 12.

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

Find the diameter of a sphere if it has a volume of $16\pi$ .

Possible Answers:

4.58

3.67

2.24

4.87

Correct answer:

4.58

Explanation:

Recall how to find the volume of a sphere:

$\text{Volume of Sphere}=\frac{4}{3}\pi r^3$ , where is the radius of the sphere.

Now, since the radius is half the diameter, the equation for the volume of a sphere can be rewritten as thus:

$\text{Volume of Sphere}=\frac{4}{3}\pi(\frac{d}{2})^3=\frac{1}{6}\pi d^3$ , where is the diameter of the sphere.

Rewrite the equation to solve for .

$d^3=\frac{6(\text{Volume of Sphere})}{\pi}$

$d=\sqrt[3]{\frac{6(\text{Volume of Sphere})}{\pi}}$

Now, plug in the volume of the sphere to find the diameter.

$d=\sqrt[3]{\frac{6(16\pi)}{\pi}}=4.58$

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

Find the diameter of a sphere if it has a volume of $24\pi$ .

Possible Answers:

8.47

1.28

9.63

5.24

Correct answer:

5.24

Explanation:

Recall how to find the volume of a sphere:

$\text{Volume of Sphere}=\frac{4}{3}\pi r^3$ , where is the radius of the sphere.

Now, since the radius is half the diameter, the equation for the volume of a sphere can be rewritten as thus:

$\text{Volume of Sphere}=\frac{4}{3}\pi(\frac{d}{2})^3=\frac{1}{6}\pi d^3$ , where is the diameter of the sphere.

Rewrite the equation to solve for .

$d^3=\frac{6(\text{Volume of Sphere})}{\pi}$

$d=\sqrt[3]{\frac{6(\text{Volume of Sphere})}{\pi}}$

Now, plug in the volume of the sphere to find the diameter.

$d=\sqrt[3]{\frac{6(24\pi)}{\pi}}=5.24$

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Example Question #9 : How To Find The Diameter Of A Sphere

Find the diameter of the sphere if it has a volume of $39\pi$ .

Possible Answers:

6.63

6.16

6.87

6.09

Correct answer:

6.16

Explanation:

Recall how to find the volume of a sphere:

$\text{Volume of Sphere}=\frac{4}{3}\pi r^3$ , where is the radius of the sphere.

Now, since the radius is half the diameter, the equation for the volume of a sphere can be rewritten as thus:

$\text{Volume of Sphere}=\frac{4}{3}\pi(\frac{d}{2})^3=\frac{1}{6}\pi d^3$ , where is the diameter of the sphere.

Rewrite the equation to solve for .

$d^3=\frac{6(\text{Volume of Sphere})}{\pi}$

$d=\sqrt[3]{\frac{6(\text{Volume of Sphere})}{\pi}}$

Now, plug in the volume of the sphere to find the diameter.

$d=\sqrt[3]{\frac{6(39\pi)}{\pi}}=6.16$

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Example Question #10 : How To Find The Diameter Of A Sphere

Find the diameter of a sphere if it has a volume of 100 .

Possible Answers:

6.95

5.22

5.76

4.41

Correct answer:

5.76

Explanation:

Recall how to find the volume of a sphere:

$\text{Volume of Sphere}=\frac{4}{3}\pi r^3$ , where is the radius of the sphere.

Now, since the radius is half the diameter, the equation for the volume of a sphere can be rewritten as thus:

$\text{Volume of Sphere}=\frac{4}{3}\pi(\frac{d}{2})^3=\frac{1}{6}\pi d^3$ , where is the diameter of the sphere.

Rewrite the equation to solve for .

$d^3=\frac{6(\text{Volume of Sphere})}{\pi}$

$d=\sqrt[3]{\frac{6(\text{Volume of Sphere})}{\pi}}$

Now, plug in the volume of the sphere to find the diameter.

$d=\sqrt[3]{\frac{6(100)}{\pi}}=5.76$

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Intermediate Geometry : How to find the diameter of a sphere

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

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

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

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

Example Question #4 : How To Find The Diameter Of A Sphere

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

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

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