Question 60

A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The difference between the surface area of the two solids, is

Solution

Surface area of the metal sheet = 2(lb + bh + hl)

= 2(27 x 8 + 8 x 1 + 1 x 27)

= 2(216 + 8 + 27)

= 2(251) = 502 cm$$^{2}$$

Edge of the cube which is formed after melting = l x b x h

i.e a$$^{3}$$ = 27 x 8 x 1 (or) a = 6

Surface area of the cube = 6a$$^{2}$$ = 216

Required difference = 502 - 216 = 286 cm$$^{2}$$

Hence, option C is the correct answer.

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