Problem 219

Problem 219

Determine the ratio of the volumes of the pair of solids shown:

Solution

Volume of inner cylinder = π r ² h

Volume of outer cylinder = π(2r) ² (2h)= π4r ² 2h=8πr² h

$\frac{inner}{outer}$ = $\frac{\pi r^{2}h}{8\pi r^{2}h}$ = $\frac{1 }{8 }$ = 1:8

Suppose length of one side of inner cube is 3l and side of outer cube is 4l

Volume of inner cube = (3l)³ = 27l ³

Volume of outer cube = (4l) ³ = 64l ³

$\frac{inner}{outer }$ = $\frac{27l^{3}}{64l^{3}}$ = $\frac{27}{64}$ = 27: 64