Question

The surface area of a sphere is 200.96 square centimeters. What is the approximate volume of the sphere? Use 3.14 for π. Round your answer to the nearest hundredth.

Answer 1

Answer:

$267.95 cm^3$

Step-by-step explanation:

We need to first find the radius of the sphere.

The surface area of a sphere is given as:

$A = 4\pi r^2$

where r is the radius

Therefore:

$200.96 = 4 * 3.14 * r^2\\\\=> r^2 = 200.96 / 12.56\\\\r^2 = 16\\\\r = \sqrt{16} \\\\r = 4cm$

The radius of the sphere is 4 cm.

The volume of a sphere is given as:

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

Therefore, the volume of the sphere of radius 4 cm is;

$V = \frac{4}{3} * 3.14 * 4^3\\\\V = 267.95 cm^3$

The volume of the sphere is $267.95 cm^3$