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)
Diagonal = s * sqrt 2.....with s(side) being 120 yds diagonal = 120 * sqrt 2 = 169.7 yds rounds to 170 yds....or if u need it in feet, it is (3 * 170) = 510 ft.
