GRE Math : How to find the surface area of a sphere

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

Find the surface area of a sphere with a diameter of 14. Use π = 22/7.

Possible Answers:

616

872

1256

428

2464

Correct answer:

616

Explanation:

Surface Area = 4πr² = 4 * 22/7 * 7² = 616

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Example Question #1531 : Gre Quantitative Reasoning

A sphere has a surface area of $16\pi$ $\displaystyle 16\pi$ square inches. If the radius is doubled, what is the surface area of the larger sphere?

Possible Answers:

$48\pi \ in^2$ $\displaystyle 48\pi \ in^2$

Cannot be determined

$64\pi \ in^2$ $\displaystyle 64\pi \ in^2$

$32\pi \ in^2$ $\displaystyle 32\pi \ in^2$

$16\pi \ in^2$ $\displaystyle 16\pi \ in^2$

Correct answer:

$64\pi \ in^2$ $\displaystyle 64\pi \ in^2$

Explanation:

The surface area of the larger sphere is NOT merely doubled from the smaller sphere, so we cannot double $16\pi$ $\displaystyle 16\pi$ to find the answer.

We can use the surface area formula to find the radius of the original sphere.

$4\pi r^2=16\pi$ $\displaystyle 4\pi r^2=16\pi$

r² = 4

r = 2

Therefore the larger sphere has a radius of 2 * 2 = 4.

The new surface area is then $4\pi \times 4^2=64\pi$ $\displaystyle 4\pi \times 4^2=64\pi$ square inches.

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

If a sphere has a volume of $36\pi$ $\displaystyle 36\pi$ cubic inches, what is its surface area?

Possible Answers:

$96\pi\ in^2$ $\displaystyle 96\pi\ in^2$

$24\pi\ in^2$ $\displaystyle 24\pi\ in^2$

$36\pi \ in^2$ $\displaystyle 36\pi \ in^2$

$32\pi\ in^2$ $\displaystyle 32\pi\ in^2$

$108\pi\ in^2$ $\displaystyle 108\pi\ in^2$

Correct answer:

$36\pi \ in^2$ $\displaystyle 36\pi \ in^2$

Explanation:

The volume of a cube is equal to $v=\frac{4}{3}\pi r^3$ $\displaystyle v=\frac{4}{3}\pi r^3$ .

So we mutiply our volume by $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ and divide by $\pi$ $\displaystyle \pi$ , giving us r=3 $\displaystyle r=3$ .

The surface area of a sphere is equal to $4\pi r^2$ $\displaystyle 4\pi r^2$ , giving us $36\pi$ $\displaystyle 36\pi$ .

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GRE Math : How to find the surface area of a sphere

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

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

Example Question #1531 : Gre Quantitative Reasoning

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

All GRE Math Resources

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