Question

A circular cylinder with a volume of 8pi m^3 is circumscribed about a right prism whose base is an equilateral triangle with one side that measures 2m. What is the altitude of the cylinder?

Answer 1

In this problem u hv to find the radius of the cylinder in order to find the altitude.To do that consider the base of the cylinder(a circle) and the base of the equilateral prism(a triangle)
now the circle is like the inner circle of a equilateral triangle,so the center of the circle will be at the centroid of the triangle which the point where all 3 medians of the triangle meet.
Using pythogarus relations median length sqrt(3). Radius will be one third of it sqrt(3)/3,
No if u equate it to the volume H = 24