Find the lateral area and surface area for a right cone whose slant height forms a 45 ̊ angle with the base whose radius is 8 mm.

lateral area = πrs = π88√2

base area = πr^2 = π*8^2
total area = 84π(1+√2)

Did you know?

Did you know that you can find the lateral area and surface area of a right cone? A right cone is a cone with its vertex directly above the center of its circular base. In this case, the slant height of the cone forms a 45 ̊ angle with the base, and the radius of the base is 8 mm. To find the lateral area, you need to calculate the circumference of the base and multiply it by the slant height. The circumference of the base is found by multiplying 2π by the radius. So, for this cone, the lateral area can be found by multiplying (2π × 8 mm) by the slant height. To find the surface area, you need to calculate the area of the base as well as the lateral area. The area of the base is found by squaring the radius and multiplying it by π. The surface area can then be found by adding the area of the base to the lateral area. By understanding these calculations, you can easily find the lateral area and surface area of a right cone, even when faced with specific angles and dimensions like in this example.

Find the lateral area and surface area for a right cone whose slant height forms a 45 ̊ angle with the base whose radius is 8 mm.

lateral area = πrs = π*8*8√2

lateral area = πrs = π88√2