Question

The length, Breadth and Height of the Cuboid are in the ratio 2:3:4 and if the total surface area is 8788 cm² then find the volume of the Cuboid.

• A. 52728 cm³
• B. 38675 cm³
• C. 66785 cm³
• D. 44544 cm³

Hint:

Apply the percentage formula directly to each term and sum the results.

Answer 1

The Correct Option is A

Let the length, breadth and height of the cuboid be in the ratio 2:3:4, written as \(2x, 3x, 4x\). The total surface area formula is \(2(lb+bh+hl) = 2(6x^2+12x^2+8x^2) = 52x^2\).
Setting this equal to the given 8788 cm² gives \(x^2 = 169\), so \(x = 13\).
The volume is then \(2x \times 3x \times 4x = 24x^3 = 24 \times 2197 = 52728\) cm³, matching option 1.