Rakesh took 5 hours to paint all sides of the cylinder. The radius and height of the cylinder are equal. The curved sides of the cylinder cut to make a right circular cone of the same height and same circular base. How much more time Rakesh needs to paint the remaining sides of the cone if his paint speed is constant?

Rakesh took 5 hours to paint all sides of the cylinder. The radius and height of the cylinder are equal. The curved sides of the cylinder cut to make a right circular cone of the same height and same circular base. How much more time Rakesh needs to paint the remaining sides of the cone if his paint speed is constant? Correct Answer 1.77 hrs

Calculation:

Let r be the radius of the cylinder and h be the height of the cylinder,

Painted area = surface area of the cylinder

⇒ 2πr (h + r)

⇒ 4πr²   (∵ h = r)

The remaining area to paint =  lateral area of the cone.

⇒ πrl

slant height, l = √(h² + r²)

⇒ √(2r²)

∴ l = r√2

∴ The remaining area to paint = πr²√2

Let t be the time taken by Rakesh to paint the remaining side,

⇒ 4πr²/5 = (πr2√2)/t

⇒ t = (5√2)/4

⇒ 1.77 hrs

Additional Information

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