Question

The DIAMETER of a sphere is doubled. What is the new volume of the sphere? A) 8 3 πr3 B) 16 3 πr3 C) 32 3 πr3 D) 64 3 πr3

Answer 1

S=4πR2

V=43πR3

To double the volume, we have to increase the radius by multiplying it by 3√2.

 let R1=R3√2
Then the volume of a sphere with radius R1 will be
V1=43πR31=43π(R3√2)3=83πR3 - twice larger than original volume.

With radius R1=R3√2 the surface area of a new sphere will be
4πR21=4πR2(3√2)2=43√4πR2

The ratio of the new surface area to the old one equals to 
43√4πR24πR2=3√4

Answer 2

32/3πr3  i just took the test and i promise this is right