Multiple choice

The length,breadth and height of a cuboid(rectangular solid) are 4:3:2 If its volume is $ 3000 {m}^{3}$, Find its surface area

  1. $1000 m^2$
  2. $1200 m^2$
  3. $1300 m^2$
  4. $1500 m^2$
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C Correct answer
Explanation

Let dimensions be 4x, 3x, 2x. Volume = 4x * 3x * 2x = 24x^3 = 3000, so x^3 = 125 and x = 5. Dimensions are 20, 15, 10. Surface area = 2(20*15 + 15*10 + 20*10) = 2(300 + 150 + 200) = 2(650) = 1300.

AI explanation

Let the length, breadth and height of the cuboid be 4x, 3x and 2x respectively. Using the volume of a cuboid formula, Volume = length * breadth * height, we get 4x * 3x * 2x = 24x^3 = 3000, so x^3 = 125 and x = 5. The dimensions are 20 m, 15 m and 10 m, and using the total surface area formula for a cuboid, 2(lb + bh + lh), we calculate 2((20 * 15) + (15 * 10) + (20 * 10)) = 2(300 + 150 + 200) = 1300 m^2. The surface area is 1300 m^2.

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