Multiple choice

The length, breadth and height of a cuboid are in the ratio $5:4:2$. If the total surface area is $1216$ c$m^2$, find the dimensions of the solid.

  1. $(21 \times 11 \times 8) $ cm
  2. $(20 \times 16 \times 8)$  cm
  3. $(27 \times 17 \times 8) $ cm
  4. $(25 \times 19 \times 8)$ cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Dimensions are 5x, 4x, 2x. TSA = 2(lw + lh + wh) = 2(20x^2 + 10x^2 + 8x^2) = 2(38x^2) = 76x^2. 76x^2 = 1216. x^2 = 16, so x = 4. Dimensions are 20, 16, 8.

AI explanation

Let the dimensions be 5x, 4x, and 2x, and use the total surface area formula for a cuboid: 2 * (lb + bh + hl) = 1216. Substituting the ratios gives 2 * (20x^2 + 8x^2 + 10x^2) = 1216, which simplifies to 76x^2 = 1216. Solving for x yields x = 4, meaning the dimensions are 20 cm by 16 cm by 8 cm.

Keep practicing — related questions