# Mathematics

A bucket full of water is in the form of a Frustum of a cone. The bottom and top radii of the Frustum are 18cm and 28cm respectively and the vertical depth is 30cm. Calculate the curved surface area, total surface area and volume of the Frustum

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1. well, I suspect the curved surface area is 2 pi * (1/2)(18+28) ,the circumference halfway up, times the slant height.

to find slant height
triangle base = 28 - 18 = 10
height = 30 so hypotenuse = sqrt (100+ 900)= 10 sqrt(10)
so area of curved surface = 46 pi * 10sqrt(10)

to get the total add pi (18^2 + 29^2)

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2. The frustrum is the bottom of a cone of height 84. The missing top has height 54.
v = π/3 (28^2*84 - 18^2*54) = 16120π cm^3

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