A company is manufacturing a new ice cube with a hole in the center, which they claim will cool a drink twice as fast as a cube of the same size. The cube has a length, width, and height of 4 cm. The hole has a diameter of 2 cm. To the nearest tenth, find the surface area of a single cube (including the inside of the hole).

Question

Mathematics

Josh Caldwell

30 September, 14:40

A company is manufacturing a new ice cube with a hole in the center, which they claim will cool a drink twice as fast as a cube of the same size. The cube has a length, width, and height of 4 cm. The hole has a diameter of 2 cm. To the nearest tenth, find the surface area of a single cube (including the inside of the hole).

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Andreas Rhodes · Answer 1

The new cube will have 7 surfaces: 4 equal square sides, 2 square surface with a hole, and one hole surface.

Area (A1) of 4 square surfaces = 4*L*W = 4*4*4 = 64 cm^2

Area (A2) of the two surfaces wit a hole = 2 (L*W - 2πd^2/4) = 2 (4*4-π*2^2/4) = 25.72 cm^2

Area (A3) of the hole = πD*W = π*2*4 = 25.13 cm^2

Total surface area, A = A1+A2+A3 = 64+25.72+25.13 = 114.85 cm^2