A school water tank is in the shape of a frustum of a cone. The height of the tank is 7.2 m and the top and bottom radii are 6m and 12 m respectively.

Question

(a) Calculate the area of the curved surface of the tank, correct to 2 decimal places.

(b) Find the capacity of the tank, in litres, correct to the nearest litre.

(c) On a certain day, the tank was filled with water. If the school has 500 students and each student uses an average of 40 litres of water per day, determine the number of days that the students would use the water.

Answer 1

Think of the frustrum as a large cone with the top missing.
Since the top radius is 1/2 the bottom radius, the missing part has 1/8 the volume of the entire cone, and the area is 1/4 that of the entire cone. The slant height is also 1/2 the slant height.

The slant height s of the entire cone would be
√(12^2 + 7.2^2) = 14
the lateral area would be π r s = π*12*14 = 196π
So, the lateral area of the frustrum would be 3/4 of that, or 126π

See what you can do with the rest, ok?

Answer 2

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