Question

the dimensions of a rectangular box are in a ratio 2:3:4 and the difference between the cost of covering it with sheet of paper at the rate of rs.4 and rs4.50 per m² is rs.416 . find the dimension of the box

Answer 1

Dimensions of rectangular box are in the ratio 2:3:4.

Let the -

• length of rectangular box = 2x
• breadth of rectangular box = 3x
• height of rectangular box = 4x

Curved surface area of cuboid = 2(lb + bh + hl)

Substitute the known values in above formula

=> 2[(2x × 3x) + (3x × 4x) + (4x × 2x)]

=> 8 (6x² + 12x² + 8x²)

=> 8(26x²)

=> 52x² m²

Now,

Cost of painting at Rs. 4 = 52x² × 4

=> Rs. 208x²

Cost of painting at Rs. 4.50 = 52x² × 4.50

=> Rs. 234x²

Difference between costs = Rs. 416

=> Rs. 234x² - Rs. 208x² = Rs. 416

=> Rs. 26x² = Rs. 416

=> 26x² = 416

=> x² = 16

=> x = 4

So,

Length of cardboard = 2x

=> 2(4)

=> 8 m

Breadth of cardboard = 3x

=> 3(4)

=> 12 m

Height of cardboard = 4x

=> 4(4)

=> 16 m

•°• Dimensions are 8m, 12m and 16m