Multiple choice

A rectangular box must hold $60$ cubic decimetres of material. Its length, breadth and height are in the ratio $3 : 4 : 5$. We have to paint all the six of its surfaces. If the paint costs $10$ rupees per square metre, then the total cost of painting the box will be:

  1. $94$ paise
  2. Rs. $1.40$
  3. Rs. $9.40$
  4. Rs. $19.40$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume = l*b*h = 3x*4x*5x = 60x^3 = 60. So x^3 = 1, x = 1. Dimensions are 3, 4, 5 dm (0.3, 0.4, 0.5 m). Surface area = 2*(0.12 + 0.20 + 0.15) = 2*(0.47) = 0.94 sq m. Cost = 0.94 * 10 = 9.40 rupees.

AI explanation

Let the dimensions be 3x, 4x, and 5x decimeters, so the volume gives the equation 60x cubed equals 60, meaning x equals 1 and the dimensions are 3, 4, and 5 decimeters. Converting these to meters gives dimensions of 0.3, 0.4, and 0.5 meters, and the total surface area is twice the sum of all unique face areas: 0.12, 0.15, and 0.20. Multiplying 2 by the sum of 0.47 gives a total surface area of 0.94 square meters. At a painting cost of 10 rupees per square meter, the total cost is 0.94 multiplied by 10, which equals 9.40 rupees.

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