The figure shows a cuboid. The area of the 3 faces A, B and C are $48$ ${c m}^{2}$ , $40$ ${c m}^{2}$ and $30$ ${c m}^{2}$ respectively. Find the volume of the cuboid.

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Solution

Let length, breadth and height of cuboid be l,b and h respectively. Then,
Area of A = $l \times b = 48 {c m}^{2}$
Area of B = $b \times h = 40 {c m}^{2}$
Area of C = $h \times l = 30 {c m}^{2}$
Now, $(A \times B \times C) = l^{2} b^{2} h^{2} = {(l b h)}^{2} = 48 \times 40 \times 30$
$\Rightarrow l b h = \sqrt{57600} = 240 {c m}^{3}$
Volume of cuboid = $l b h = 240 {c m}^{3}$

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