The edges of a cuboid are in the ratio 4 : 3 : 2 and its total surface area is 208 cm2. What is the volume of the cuboid?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 192 cm3
The total surface area of a cuboid is \(2(lb+bh+hl)\) and its volume is \(l\times b\times h\). Take the edges as \(4k\), \(3k\) and \(2k\), find \(k\) from the surface area, then multiply the edges.
\(lb+bh+hl=12k^2+6k^2+8k^2=26k^2\)
Surface area \(=2\times26k^2=52k^2=208\)
\(k^2=4\), so \(k=2\) (a length is positive)
Edges: 8 cm, 6 cm and 4 cm
Volume \(=8\times6\times4=192\) cm3
