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ACT Math : Solid Geometry

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

What is the surface area of a sphere that has a diameter of eight inches? Reduce any fractions in your answer and leave your answer in terms of $\pi$ .

Possible Answers:

$\frac{2048}{3} \pi inches^3$

$64\pi inches^2$

$256 \pi inches^3$

$64 \pi inches^3$

$256 \pi inches^2$

Correct answer:

$64\pi inches^2$

Explanation:

To find the volume of a sphere area of a sphere plug the radius into the following formula given by :

$SA = 4\pi r^2$ .

To find the radius given the diameter, divide the diameter by 2.

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

$r=\frac{8}{2}=4$
Thus:
$SA = 4\pi 4^2 = 64 \pi inches^2$

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

What is the surface area of a sphere, in inches, that has a surface area equal to its volume? Leave your answer in terms of $\pi$ .

Possible Answers:

$9\pi in^2$

$108\pi in^2$

$27\pi in^2$

$36\pi in^3$

$36\pi in^2$

Correct answer:

$36\pi in^2$

Explanation:

To find the radius of a sphere that has a volume equal to it's surface area, begin by setting the volume and surface area formulas for a sphere equal to each other and solving for the radius:
$\\\frac{4}{3}\pi r^3 = 4\pi r^2 \newline \newline \frac{4}{3}r^3 = 4r^2 \newline \newline 4r^3 = 12r^2 \newline r^3 = 3r^2 \newline r = 3$

Next we plug the answer for our radius into the formula for the surface area:

$4\pi 3^2 = 36\pi in^2$ , remember to check the units.

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

Find the surface area of a sphere whose radius is .

Possible Answers:

$108\pi$

$4\pi$

$36\pi$

$12\pi$

Correct answer:

$36\pi$

Explanation:

To solve, simply remember the following formula:

$SA=4\pi{r^2}=4*\pi*3^2=36\pi$

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

Find the surface area of a sphere whose radius is . Thus,

Possible Answers:

$48\pi$

$12\pi$

$32\pi$

$36\pi$

Correct answer:

$36\pi$

Explanation:

To find surface area, simply use the formula. Thus,

$SA=4\pi{r^2}=4\cdot\pi\cdot3^2=4\cdot\pi\cdot9=36\pi$

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

Find the surface area of a sphere whose side diameter is .

Possible Answers:

$4\pi$

$2\pi$

$3\pi$

$8\pi$

Correct answer:

$4\pi$

Explanation:

To solve, simply use the following formula for the surface area of a circle. Thus,

$SA=4\pi{r^2}=4*\pi*1^2=4\pi$

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Example Question #731 : Geometry

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

300π

615π

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 #1 : How To Find The Volume Of A Sphere

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:

3468.05 cu.in.

8557.46 cu.in.

138.43 cu.in.

434.19 cu.in.

92.48 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 : How To Find The Volume Of A Sphere

The radius of a sphere is . What is the approximate volume of this sphere?

Possible Answers:

$20\pi$

$288\pi$

$516\pi$

$300\pi$

$138\pi$

Correct answer:

$288\pi$

Explanation:

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

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

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

$V=288\pi$

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

A cube has a side dimension of 4. A sphere has a radius of 3. What is the volume of the two combined, if the cube is balanced on top of the sphere?

Possible Answers:

$4 + 36\pi$

$16 + 36\pi$

$16 + 6\pi$

$64 + 36\pi$

$64 + 6\pi$

Correct answer:

$64 + 36\pi$

Explanation:

$V_{cube}=(\text{side})^3=(4)^3=64$

$V_{sphere}=\frac{4}{3}\pi r^3=\frac{4}{3}\pi(3^3)=\frac{4}{3}\pi(27)=36\pi$

$V_{total}=64+36\pi$

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

What is the volume of a sphere with a diameter of 6 in?

Possible Answers:

$72\pi\ in^{3}$

$36\pi\ in^{3}$

$108\pi\ in^{3}$

$288\pi\ in^{3}$

$216\pi\ in^{3}$

Correct answer:

$36\pi\ in^{3}$

Explanation:

The formula for the volume of a sphere is:

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

where = radius. The diameter is 6 in, so the radius will be 3 in.

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ACT Math : Solid Geometry

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

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

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

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

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

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

Example Question #731 : Geometry

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 #3 : How To Find The Volume Of A Sphere

All ACT Math Resources

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