How to find the surface area of a sphere

Help Questions

GRE Quantitative Reasoning › How to find the surface area of a sphere

Questions 1 - 3

1

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

2464

616

1256

428

872

Explanation

Surface Area = 4_πr_2 = 4 * 22/7 * 72 = 616

2

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

$32\pi \ in^2$

$64\pi \ in^2$

$48\pi \ in^2$

$16\pi \ in^2$

Cannot be determined

Explanation

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

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

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

_r_2 = 4

r = 2

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

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

3

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

$36\pi \ in^2$

$32\pi\ in^2$

$108\pi\ in^2$

$24\pi\ in^2$

$96\pi\ in^2$

Explanation

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

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

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

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