Determine the volume of a cube whose total surface area is $432, cm^{2}$ .

medium 3 marks Class 8 · Mathematics · Cubes and Cube Roots

Answer

4322, cm^{3}

The correct answer is $4322, cm^{3}$ — Compute the volume $V = a^{3} = (62)^{3} = 216, (22) = 4322, cm^{3}$ .

Step-by-step solution

Use the formula $S = 6 a^{2}$ for the surface area of a cube, giving $6 a^{2} = 432$ .
Solve for $a^{2}$ : $a^{2} = 72$ .
Take the square root: $a = 72 = 62, cm$ .
Compute the volume $V = a^{3} = (62)^{3} = 216, (22) = 4322, cm^{3}$ .

Common mistake: Dividing the surface area by 6 incorrectly or ignoring the exponent when finding

a

Concept tested: Volume from surface area