Question

A right circular solid cone and solid cylinder of same radius (r) and height (h) melted to create a solid cylinder of same height. What is the radius of new cylinder in terms of the radius of old cylinder
1. 1.01r
2. 1.1r
3. 1.15r
4. 1.23r

Answer 1

Correct Answer - Option 3 : 1.15r

Calculation:

Total volume to be melted = (1/3)πr²h + πr²h

⇒ 4πr²h/3

Let R be radius of new cylinder,

Volume = πR²h

⇒ πR2h = 4πr2h/3

⇒ R = 2r/√3

⇒ R = 1.15r 

When a solid cut into smaller pieces or melted to form solids, the total volume before and after won't change. But total surface area may change. 

The total surface area of a cylinder is the sum of curved surface area and base areas.

The volume of the cylinder is the product of the base area and height of the cylinder.

The total surface area of a circular cylinder with height h and base radius r given by 2πr(r + h).

The curved surface area of a circular cylinder is equal to 2πrh.

The total surface area of a right circular cone of slant height L and radius r is given by πr(L + r).

The volume of right circular cone is given by πr²h/3, where h is height of the cone.