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A cake as shown has three layers, each of which is a cuboid as shown. The bases of these cuboids are squares whose sides are of lengths 15 cm, 30 cm and 45 cm. The height of each layer is 5 cm. Find the total area of the cake that must be frosted. Assume that there will be frosting between the layers, but not at the bottom of the cake.

(a) 5000 cm

(b) 4000 cm

(c) 4950 cm

(d) 4500 cm

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(c) 4950 cm2

Area of the cake to be frosted 

= Area of tops of (cuboid A + cuboid B + cuboid C) + Area of four sides of (cuboid A + cuboid B + cuboid C) 

= (152 + 302+ 452) cm2 + [2(15 × 5 + 15 × 5)] + [2 (30 × 5 + 30 × 5)] + [2(45 × 5 + 45 × 5 )] = (225 + 900 + 2025) cm2 + (300 + 600 + 900) cm2 = 4950 cm2.

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