Calculate the total surface area of a cone of height 12cm and base radius 5cm

Answer 1

Total surface area of a cone = πr(r + l)

where r is the base radius and l is the slant height of the cone.

Given that the height of the cone is 12cm and the base radius is 5cm, we need to find the slant height first.

Using the Pythagorean theorem, we can find the slant height:

l^2 = r^2 + h^2
l^2 = 5^2 + 12^2
l^2 = 25 + 144
l^2 = 169
l = √169
l = 13 cm

Now we can calculate the total surface area of the cone:

Total surface area = π(5)(5 + 13)
Total surface area = π(5)(18)
Total surface area = 90π

Therefore, the total surface area of the cone is 90π square centimeters.