Let V and A denote the volume and surface area of a cuboid of dimensions a, b and c units respectively. Which one is correct?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\frac{A}{V}=\left(\frac{2}{a}+\frac{2}{b}+\frac{2}{c}\right)\)
A cuboid of dimensions a, b and c has volume abc and total surface area 2(ab + bc + ca), its six faces being three pairs of equal rectangles. Dividing each term of the area by abc cancels two of the letters:
\(V=abc\), \(A=2(ab+bc+ca)\)
\(\displaystyle\frac{A}{V}=\frac{2ab}{abc}+\frac{2bc}{abc}+\frac{2ca}{abc}\)
\(\displaystyle\frac{A}{V}=\frac{2}{c}+\frac{2}{a}+\frac{2}{b}\)