Question

Geometry question, i appreciate any help!

Answer 1

Remark
The easiest way to do this is to find the radius of both spheres . That gives you the scale factor. The answer to the next two parts might surprise you.

Step one
Find the volume of the small sphere.
V = 4/3 pi r^3
V = 250 yards^3
pi = 3.14
r = ???

Sub and solve
250 = 4/3 pi * r^3  Multiply both sides by 3/4 to get rid of the fraction on the right.

250 * 3/4 = pi * r^3
187.5 = pi r^3   Divide by pi
187.5 / pi = r^3  
59.71 = r^3   Take the cube root of both sides.
cube root (59.71) = cube root(r^3)
r = 3.91

Step 2
find the radius of the large sphere.
I'm just going to give you the answer. Follow the above steps to confirm it.
V = 686 cubic yards
pi = 3.14
r = ??
r = cube root (514.5/3.14)
r = 5.472

Step 3
Find the ratio
r_large/r_small = 5.472/3.91 = 1.3995

I'm going to leave the Area calculations to you
The area ratios should come to 1.96 (about)

The volume ratios should come to 1:2.74