The radius of base of a cone is $5$ cm and height of the cone is $12$ cm. find its curved surface area
- $204.3\ \text{ cm }^{ 2 }$(approx)
- $102.8\ \text{ cm }^{ 2 }$(approx)
- $40.8\ \text{ cm }^{ 2 }$(approx)
- $52\ \text{ cm }^{ 2 }$(approx)
Curved surface area of a cone is pi * r * l, where l = sqrt(r^2 + h^2). With r=5 and h=12, l = sqrt(25 + 144) = 13. Area = 3.14 * 5 * 13 = 204.1. Option A is the closest.
First find the slant height using the Pythagorean theorem, since the square of the slant height equals the square of the radius plus the square of the height. The slant height squared is five squared plus twelve squared, equaling twenty five plus one hundred forty four, which gives a slant height of thirteen centimeters. The curved surface area of a cone is pi times the radius times the slant height, so the area is twenty two by seven times five centimeters times thirteen centimeters, which equals two hundred four point three square centimeters.