A sandcastle in the shape of a truncated cone. Calculate the diameter of the base.

The diamètre of the top is 20cm, the slope length is 32cm and the height is 30cm.

Based on the given above, since the upper diameter, height and lateral height are given, through illustration, it can be said that the diameter of the base is equal to the upper diameter plus twice the lower base of the two right triangles formed by the height and the lateral edge, in other words,

D=d+2 (x); d=20 and x=base of the right triangle,

by pythagorean theorem, 32 = sqrt of x^2 + 30^2; x = 11.1355

Therefore the diameter of the lower base = 20+2 (11.1355) = 42.27 cm