Question

The diameter of a large sphere is 4 times the diameter of a small sphere. The surface area of the large sphere is how many times the surface area of small sphere?

Answer 1

Surface Area of a Sphere = 4π(d/2)²
Let the smaller sphere's diameter be just a sample of 4 units in diameter and let the large spheres diameter be 4 times that of the smaller sphere.

Small Sphere: 4π(4/2)² = 16π units²
Large Sphere: 4π(16/2)² = 256π units²

256π / 16π = 16 times

The large sphere has a surface area 16 times that of the smaller one.