The edges of a cuboid are in the ratio 3 : 2 : 1 and its total surface area is 352 cm2. What is the volume of the cuboid?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 384 cm3
Write the edges as \(3k\), \(2k\) and \(k\). The total surface area \(2(lb+bh+lh)\) then gives \(k\), and the volume is \(lbh\).
\(2\left(3k\cdot2k+2k\cdot k+3k\cdot k\right)=2(6k^2+2k^2+3k^2)=22k^2\)
\(22k^2=352\), so \(k^2=16\) and \(k=4\)
Edges: 12 cm, 8 cm and 4 cm
Volume \(=12\times8\times4=384\) cm3
