Your classmate claims that if you

double the radius of a sphere, its surface area and

volume will quadruple. What is your classmate's

error? Explain.

SA of a sphere is 4πr² Using a sample of radius 3 the SA would be 36π²

(4πx3²) If we double the radius and make it 6, the SA would be 144π²

So for Surface area, your classmate is correct.

What about the volume? V of a Sphere = 4/3 π r³

Again using 3 the Volume of a Sphere with radius 3 = 4/3 π 27

But the volume of a sphere with radius 6 = 4/3 π 216 which is eight times the volume of the smaller sphere. (27 x 8 = 216) So your friend is right about Surface Area but wrong about the volume.