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

Correct answer: B. 286 cm2

  • A. 284 cm2
  • B. 286 cm2
  • C. 296 cm2
  • D. 300 cm2

Explanation

The melted sheet has volume 27 cm x 8 cm x 1 cm = 216 cm3, so the cube edge is cube root of 216 cm3 = 6 cm. The sheet surface area is 2(27 x 8 + 8 x 1 + 27 x 1) cm2 = 502 cm2, and the cube surface area is 6 x 6^2 cm2 = 216 cm2. Their difference is 502 cm2 - 216 cm2 = 286 cm2; 284 cm2 is the likely arithmetic error.

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About Area and Volume

Area measures the surface enclosed by two-dimensional figures, while volume measures the space occupied by three-dimensional solids. Problems use formulas for rectangles, triangles, circles, prisms, cylinders, cones, spheres, and composite figures, including unit conversion and the distinction between surface area, lateral area, and volume.

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