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Intermediate Geometry : How to find the diameter of a sphere

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Example Questions

Example Question #11 : How To Find The Diameter Of A Sphere

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

Possible Answers:

3.26

3.69

3.94

3.08

Correct answer:

3.94

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.

$d=\sqrt[3]{\frac{6(32)}{\pi}}=3.94$

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Example Question #11 : How To Find The Diameter Of A Sphere

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

Possible Answers:

5.24

5.56

5.70

5.69

Correct answer:

5.56

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.

$d=\sqrt[3]{\frac{6(90)}{\pi}}=5.56$

Make sure to round to places after the decimal.

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Example Question #12 : How To Find The Diameter Of A Sphere

Find the diameter of a sphere if it has a volume of $106\pi$ .

Possible Answers:

8.60

7.89

8.99

9.06

Correct answer:

8.60

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.

$d=\sqrt[3]{\frac{6(106\pi)}{\pi}}=8.60$

Make sure to round to places after the decimal.

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Example Question #13 : How To Find The Diameter Of A Sphere

Find the diameter of a sphere that has a volume of $69\pi$ .

Possible Answers:

7.45

6.20

7.93

8.22

Correct answer:

7.45

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.

$d=\sqrt[3]{\frac{6(69\pi)}{\pi}}=7.45$

Make sure to round to places after the decimal.

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Example Question #11 : How To Find The Diameter Of A Sphere

Find the diameter of a sphere if it has a volume of $650\pi$ .

Possible Answers:

16.19

12.28

12.11

15.74

Correct answer:

15.74

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.

$d=\sqrt[3]{\frac{6(650\pi)}{\pi}}=15.74$

Make sure to round to places after the decimal.

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Example Question #15 : How To Find The Diameter Of A Sphere

Find the diameter of a sphere if it has a volume of $887\pi$ .

Possible Answers:

17.46

18.11

17.55

16.28

Correct answer:

17.46

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.

$d=\sqrt[3]{\frac{6(887\pi)}{\pi}}=17.46$

Make sure to round to places after the decimal.

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Example Question #12 : How To Find The Diameter Of A Sphere

Find the diameter of a sphere if its volume is .

Possible Answers:

4.86

4.95

4.20

4.44

Correct answer:

4.86

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.

$d=\sqrt[3]{\frac{6(60)}{\pi}}=4.86$

Make sure to round to places after the decimal.

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Example Question #13 : How To Find The Diameter Of A Sphere

Find the diameter of a sphere if it has a volume of 908 .

Possible Answers:

6.58

12.62

6.448.75

12.01

Correct answer:

12.01

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.

$d=\sqrt[3]{\frac{6(908)}{\pi}}=12.01$

Make sure to round to places after the decimal.

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Example Question #14 : How To Find The Diameter Of A Sphere

A company wants to construct an advertising balloon spherical in shape. It can afford to buy 28,000 square meters of material to make the balloon. What is the largest possible diameter of this balloon (nearest whole meter)?

Possible Answers:

$68\;m$

$94\;m$

$76\;m$

$47\;m$

$38\;m$

Correct answer:

$94\;m$

Explanation:

This is equivalent to asking the diameter of a balloon with surface area 28,000 square meters.

The relationship between the surface area and the radius is:

$A=4\pi r^{2}$

To find the radius, substitute for the surface area, then solve:

$28,000=4\pi r^{2}$

$r^{2}=\frac{28,000}{4\pi }$

$r=\sqrt{\frac{28,000}{4\pi }}\approx47$

To find the diameter , double the radius—this is 94.

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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 #11 : How To Find The Diameter Of A Sphere

Example Question #11 : How To Find The Diameter Of A Sphere

Example Question #12 : How To Find The Diameter Of A Sphere

Example Question #13 : How To Find The Diameter Of A Sphere

Example Question #11 : How To Find The Diameter Of A Sphere

Example Question #15 : How To Find The Diameter Of A Sphere

Example Question #12 : How To Find The Diameter Of A Sphere

Example Question #13 : How To Find The Diameter Of A Sphere

Example Question #14 : How To Find The Diameter Of A Sphere

All Intermediate Geometry Resources

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