A water tank is made by joining a cone of height 4 cm to the base of a cylinder of height 8 cm. Both have radius 3 cm. What is the total surface area of the outside of the tank, excluding the circular join?

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Question

A water tank is made by joining a cone of height 4 cm to the base of a cylinder of height 8 cm. Both have radius 3 cm. What is the total surface area of the outside of the tank, excluding the circular join?

Accepted Answer

63π cm² — Award 1 mark for correct method and calculation. Curved surface area of cylinder = 2πrh = 2π × 3 × 8 = 48π cm². Slant height of cone = √(3² + 4²) = 5 cm. Curved surface area of cone = πrl = π × 3 × 5 = 15π cm². Total = 48π + 15π = 63π cm². A is incorrect — introduces unnecessary surd. B and D are incorrect presentations of the same answer without simplification.

Answer

63π cm²

Answer

48π + 15π cm²

Answer

(48 + 15)π cm²

Answer

15π(3 + √5) cm²

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