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High School Math : Spheres

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Example Questions

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

What is the volume of a sphere with a radius of ?

Possible Answers:

$144\pi$

$2304\pi$

$1728\pi$

$1600\pi$

Correct answer:

$2304\pi$

Explanation:

To solve for the volume of a sphere, you must first know the equation for the volume of a sphere.

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

In this equation, is equal to the radius. We can plug the given radius from the question into the equation for .

$V=\frac{4}{3}(\pi)(12^{3})$

Now we simply solve for .

$V=\frac{4}{3}(\pi)(1728)$

$V=(\pi)(2304)=2304\pi$

The volume of the sphere is $2304\pi$ .

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

What is the volume of a sphere with a radius of 4? (Round to the nearest tenth)

Possible Answers:

$75.3\pi$

$85.3\pi$

$75.9\pi$

$91.2\pi$

Correct answer:

$85.3\pi$

Explanation:

To solve for the volume of a sphere you must first know the equation for the volume of a sphere.

The equation is

Then plug the radius into the equation for yielding

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

Then cube the radius to get

$V=\frac{4}{3}(64)\pi$

Multiply the answer by $\frac{4}{3}$ and to yield $85.3\pi$ .

The answer is $85.3\pi$ .

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

For a sphere the volume is given by V = (4/3)πr³ and the surface area is given by A = 4πr². If the sphere has a surface area of 256π, what is the volume?

Possible Answers:

750π

615π

300π

683π

Correct answer:

683π

Explanation:

Given the surface area, we can solve for the radius and then solve for the volume.

4πr² = 256π

4r² = 256

r² = 64

r = 8

Now solve the volume equation, substituting for r:

V = (4/3)π(8)³

V = (4/3)π*512

V = (2048/3)π

V = 683π

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

Circle_with_diameter

A typical baseball is 76mm in diameter. Find the baseball's volume in cubic centimeters.

Possible Answers:

$22984.7cm^{3}$

$2786cm^{3}$

$1838cm^{3}$

Not enough information to solve

$230cm^{3}$

Correct answer:

$230cm^{3}$

Explanation:

In order to find the volume of a sphere, use the formula

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

We were given the baseball's diameter, $\dpi{100} D=76mm$ , which must be converted to its radius.

D=2r

76mm=2r

$r=\frac{76mm}{2}$

$\rightarrow 38mm$

Now we can solve for volume.

$V=\frac{4}{3}\pi (38mm)^{3}$

$V=\frac{4}{3}\pi (54872mm^{3})$

$V=73162\frac{2}{3}mm^{3}*\pi$

$\rightarrow 229847.30mm^{3}$

Convert to centimeters.

$\dpi{100} \frac{229847.30mm^{3}}{1}*\frac{1cm^{3}}{1000mm^{3}}\approx 230cm^{3}$

If you arrived at $1838cm^{3}$ then you did not convert the diameter to a radius.

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

What is the volume of a sphere whose radius is r=1.6in .

Possible Answers:

$\dpi{100} 16.17in^{3}$

$\dpi{100} 9.65in^{3}$

Not enough information to solve

$17.16in^{3}$

$\dpi{100} \dpi{100} 6.59in^{3}$

Correct answer:

$17.16in^{3}$

Explanation:

In order to find the volume of a sphere, use the formula

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

We were given the radius of the sphere, r=1.6in .Therefore, we can solve for volume.

$\dpi{100} V=\frac{4}{3}\pi (1.6in)^{3}$

$\dpi{100} V=\frac{4}{3}\pi (4.096in^{3})$

$\dpi{100} V=17.16in^{3}$

If you calculated the volume to be $\dpi{100} 9.65in^{3}$ then you multiplied by $\frac{3}{4}$ rather than by $\frac{4}{3}$ .

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

To the nearest tenth of a cubic centimeter, give the volume of a sphere with surface area 1,000 square centimeters.

Possible Answers:

$743.4 \textrm{ cm}^{3}$

$785.4\textrm{ cm}^{3}$

$3,141.6\textrm{ cm}^{3}$

$2,973.5 \textrm{ cm}^{3}$

$991.2\textrm{ cm}^{3}$

Correct answer:

$2,973.5 \textrm{ cm}^{3}$

Explanation:

The surface area of a sphere in terms of its radius is

$A = 4\pi r^2$

Substitute A = 1,000 and solve for :

$4\pi r^2 =A$

$4\pi r^2 =1,000$

$r^2 =\frac{1,000}{4\pi } = \frac{250}{\pi }$

$r =\sqrt{ \frac{250}{\pi }} \approx 8.92 \textrm{ cm }$

Substitute for in the formula for the volume of a sphere:

$V = \frac{4\pi r^3}{3} \approx\frac{4\pi \cdot 8.92^3}{3} \approx 2,973.5 \textrm{ cm }^{3}$

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

Find the volume of the following sphere.

Sphere

Possible Answers:

$270 \pi m^3$

$312 \pi m^3$

$300 \pi m^3$

$288 \pi m^3$

$360 \pi m^3$

Correct answer:

$288 \pi m^3$

Explanation:

The formula for the volume of a sphere is:

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

where is the radius of the sphere.

Plugging in our values, we get:

$V=\frac{4}{3} \pi (6m)^3$

$V=\frac{4}{3} \pi 216m^3 = 288 \pi m^3$

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

Find the volume of the following sphere.

Sphere

Possible Answers:

$952 \pi m^3$

$992 \pi m^3$

$982 \pi m^3$

$962 \pi m^3$

$972 \pi m^3$

Correct answer:

$972 \pi m^3$

Explanation:

The formula for the volume of a sphere is:

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

Where is the radius of the sphere

Plugging in our values, we get:

$V = \frac{4 \pi (9m)^3}{3}$

$V = 972 \pi m^3$

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Example Question #1 : Spheres

The specifications of an official NBA basketball are that it must be 29.5 inches in circumference and weigh 22 ounces. What is the approximate volume of the basketball? Remember that the volume of a sphere is calculated by V=(4πr³)/3

Possible Answers:

138.43 cu.in.

8557.46 cu.in.

3468.05 cu.in.

92.48 cu.in.

434.19 cu.in.

Correct answer:

434.19 cu.in.

Explanation:

To find your answer, we would use the formula: C=2πr. We are given that C = 29.5. Thus we can plug in to get [29.5]=2πr and then multiply 2π to get 29.5=(6.28)r. Lastly, we divide both sides by 6.28 to get 4.70=r. Then we would plug into the formula for volume V=(4π〖(4.7)〗³) / 3 (The information given of 22 ounces is useless)

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Example Question #1 : Spheres

What is the volume of a sphere with a diameter of ?

Possible Answers:

$288\pi$

$1152\pi$

$2304\pi$

$24\pi$

$48\pi$

Correct answer:

$288\pi$

Explanation:

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

The problem gives us the diameter, however, and not the radius. Since the diameter is twice the radius, or d=2r , we can find the radius.

12=2r

$\frac{12}{2}=r$

6=r .

Now plug that into our initial equation.

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

$V=\frac{4}{3}\pi (6)^3$

$V=\frac{4}{3}\pi(216)$

$V=288\pi$

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University of North Texas, Doctor of Philosophy, Materials Engineering.

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High School Math : Spheres

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

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

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

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

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

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

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

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

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

Example Question #1 : Spheres

Example Question #1 : Spheres

All High School Math Resources

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