Question

A conveyor belt drops gravel to create a pile in the shape of a right circular cone. The cone is formed from 3,200 ft^3 of gravel. If the height of the cone is 24ft, what is the radius, in feet, of the base cone? Round your answer to the nearest tenth of a foot.

Answer 1

11.3 ft

Explanation:

`V_(gravel)=3,200\: ft^3\\\\height \:(h) =24\: ft\\\\ To \: find:\: radius\:(r)`

Since, gravel is in the shape of right circular cone.

`\implies V_(gravel)= (1)/(3)\pi r^2 h\\\\\implies 3,200= (1)/(3)(3.14) r^2 (24)\\\\\implies r^2=(3,200* 3)/(3.14* 24)\\\\\implies r^2=(9,600)/(75.36)\\\\\implies r^2=127.388535\\\\\implies r=\pm√(127.388535)\\\\\implies r=\pm 11.286653\\radius\: can't\: be\: negative\\\\\implies r=11.286653\\\\\implies r \approx 11.3 \: ft`