Question

The volumes of two spheres are 327 π in3and 8829 π in3.

a.What is the ratio of their radii?
b.What is the ratio of their surface areas?

Answer 1

a) Volume of the first sphere V1=4/3πr(1)³
Volume of the second sphere V2=4/3πr(2)³

V1/V2= 4/3πr³(1)/4/3πr³(2)
V1/V2= r³(1)/r³(2)

At the same time V1/V2=327π/8829π=327/8829=1/27
V1/V2= r³(1)/r³(2) =1/27
r(1)/r(2)=1/3

b) SA(1)= 4πr²(1) SA -surface area
SA(2)= 4πr²(2)

SA(1)/SA(2) = 4πr²(1)/4πr²(2) = r²(1)/r²(2)
SA(1)/SA(2) = r²(1)/r²(2) = ((r(1)/r(2))² =(1/3)²=1/9
SA(1)/SA(2)=1/9