Question

Find the lateral and total surface area for the cone. If necessary, round to the nearest tenth and leave theanswer in terms of t.25 cm22.2 cmThe lateral area isIr cm?The surface area isit cm?

Answer 1

The lateral surface area is 277.5 square centimeters , the total surface area is 400.71 square centimeters

Here, we want to find the lateral area and the surface area of the cone

Mathematically, the formula for the lateral area of a cone is given below;

`S\text{ = }\pi rl`

where r represents the radius of the cone and l represents the slant height of the cone

In the diagram given, the slant height l of the cone is 25 cm while the diameter of the base of the cone is 22.2 cm

The formula for the radius of the cone = length of diamter/2

So the radius of the cone is 22.2 cm/2 = 11.1 cm

Thus the lateral area is;

`S\text{ = }\pi\text{ }*\text{ 11.1 cm }*25cm=277.5cm^2`

Mathematically, the total surface area of a cone is the area of the base of the cone added to the area of the base of the cone

The area of the base of the cone is;

`S\text{ = }\pi* r^2`

The radius of the cone is 11.1 cm

Thus, the area of the base = π * 11.1^2 = 123.21 square centimeters

So the total surface area of the cone is (277.5 + 123.21) = 400.71 square centimeters