The curved surface area of a cylindrical pillar is and its volume is . Find the diameter and the height of the pillar.
Step 1: Find equation for height of the pillar
Given, curved surface area of cylindrical pillar
We know that, curved surface area of cylinder , where, is the radius of cylindrical pillar and is height
By the problem,
Step 2: Find radius of the pillar
Given, volume of cylindrical pillar
We know that volume of cylinder
By the problem,
Radius of the cylindrical pillar
Step 3: Find the diameter and the height of the pillar
Diameter of the pillar
Height of the pillar
Hence, the diameter and the height of the pillar is and respectively.