Question

Calculate the total surface area and the volume of a cone of base diameter 9cm and slant height of 12cm

Answer 1

T.S.A = 233.29 cm²

volume of the cone = 235.84 cm³

Explanation:

Given;

diameter of the cone, d = 9 cm

radius of the cone, r = 4.5 cm

slant height of the cone, l = 12 cm

The total surface of the cone is calculated as;

T.S.A = πr² + πrl

T.S.A = πr(r + l)

T.S.A = 3.142 x 4.5(4.5 + 12)

T.S.A = 233.29 cm²

The volume of the cone is calculated as;

`V = (1)/(3) \pi r^2h`

Where;

h is height of the cone

h² = 12² - 4.5²

h² = 123.75

h = √123.75

h = 11.12 cm

`V = (1)/(3) \pi * (4.5)^2 * 11.12\\\\V = 235.84 \ cm^3`