The areas of three adjacent faces of a cuboidal box are 96 cm2, 48 cm2 and 72 cm2, respectively. The volume of the box is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 576 cm3
If the edges are \(l\), \(b\) and \(h\), the three adjacent faces have areas \(lb\), \(bh\) and \(hl\). Their product is \(l^2b^2h^2\), the square of the volume \(lbh\).
\(V^2=96\times48\times72=331776\)
\(V=\sqrt{331776}=576\) cm3
Shortcut: Factorise the three areas instead of multiplying them out.
\(96\times48\times72=(2^{5}\times3)\times(2^{4}\times3)\times(2^{3}\times3^{2})=2^{12}\times3^{4}\)
\(V=2^{6}\times3^{2}=64\times9=576\) cm3