Mia, Mikes’ little sister, plays in a sandbox. She wants to make a huge sand cake in the shape of truncated cone of height 1 ft. The low base should have radius 2 ft, and the upper base - radius 1 ft. How much work should Mia put on this project? The density of the sand is 100 lb/ft3, acceleration due to gravity is 32 ft/s2, and Mia constructs the cake taking the sand from the ground. Solve the problem along the following lines:
Mia, Mikes’ little sister, plays in a sandbox. She wants to make a huge sand cake in the shape of truncated cone of height 1 ft. The low base should have radius 2 ft, and the upper base - radius 1 ft. How much work should Mia put on this project? The density of the sand is 100 lb/ft3, acceleration due to gravity is 32 ft/s2, and Mia constructs the cake taking the sand from the ground. Solve the problem along the following lines:
(a) On the truncated cone, show the given dimensions. Draw a typical thin horizontal layer, introduce variables, and determine the dimensions of the layer.
(b) For this layer, determine the volume, mass, weight, and work required to lift the sand to the level of the layer.
(c) Set up the integral for the total work and calculate this integral. You are not allowed to use integral calculators, but you may use a calculator to multiply numbers.
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