The radius of the base of a right circular cone is 27 centimeters and its slant height is 38 centimeters. What, in terms of 𝜋, is its total surface area?
The total surface area of a cone can be calculated by adding the base area to the area of the curved surface. As the base of a cone is a circle, we can calculate this area using the formula 𝜋𝑟 squared. We calculate the area of the curved surface using the formula 𝜋𝑟𝐿, where 𝐿 is the slant height of the cone.
In our example, the radius of the base is 27 centimeters. Therefore, we can work out the base area by multiplying 𝜋 by 27 squared. 27 squared is equal to 729. Therefore, the base area is 729𝜋. To calculate the area of the curved surface, we will use the formula 𝜋𝑟𝐿, where 𝑟 is the radius, in this case 27 centimeters, and 𝐿 is the slant height, 38 centimeters.
27 multiplied by 38 is 1026. Therefore, the area of the curved surface is 1026𝜋. Adding 729𝜋 and 1026𝜋 gives us 1755𝜋. This means that the total surface area of a cone with radius 27 centimeters and slant height 38 centimeters is 1755𝜋.