A sphere has a surface area of 144 square centimeters. The volume of the sphere is k cubic centimeters. What is the value of k?

SAT Area and volume Practice Question 13 (Hard)

Math · Geometry and TrigonometryHard

A sphere has a surface area of $144\pi$ square centimeters. The volume of the sphere is $k\pi$ cubic centimeters. What is the value of $k$ ?

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Answer: 288

The surface area of a sphere is $4\pi r^2$ , so $4\pi r^2 = 144\pi$ and $r^2 = 36$ , giving $r = 6$ . The volume is $\frac{4}{3}\pi r^3 = \frac{4}{3}\pi(216) = 288\pi$ . So $k = 288$ .

Using $r = 12$ (from $\pi r^2 = 144\pi$ ) treats the surface area formula like the area of a circle and greatly overstates the volume.

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