Volumes Practice Test 2

Here, lb : bh : hl = 2 : 3 : 4; then
$\frac{\mathit{l}\mathit{b}}{\mathit{b}\mathit{h}}$ = $\frac{2}{3}$
⇒ l : h = 2 : 3 and also , $\frac{\mathit{l}\mathit{h}}{\mathit{b}\mathit{h}}$ = $\frac{4}{3}$
∴ l : b = 4 : 3
From these two, we get, l : b : h = 4 : 3 : 6
Let sides of rectangular block are 4x, 3x and 6x cm respectively, then
4x × 3x × 6x = 9000
⇒ ${\mathit{x}}^3$ = $\frac{9000}{4\times 3\times 6}$ = 125
∴ x = 5
Hence, shortest side = 3x = 3 × 5 = 15 cm