2 similar figures, volumes given, surface are of larger figure given SA of smaller

Question

volume 27in

V 127in

SA 63in

Answer 1

Volume ratios are R^3:1 and surface area ratios are R^2:1 where R is the common ratio of the sides. If volumes are 127 cu in and 27, the ratio is 127/27=R^3, so R=1.6755 (cube root of 127/27). From this R^2=2.8073. So the surface area of the larger figure is 2.8073*63=176.86 sq in. All figures approximate.