Question

A cone has a height of `8 cm` and its base has a radius of `4 cm`. If the cone is horizontally cut into two segments `3 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

T S A = 138.3926 `cm^2`

Explanation:

`OA = h = 8 cm, OB r = 4 cm, , AF = h_1 = 8-3 = 5 cm`

`FD = r_2 =( h_1 /h)*r = (5/ 8) * 4 = 2.5 cm`

`AC = l = sqrt(h^2 + r^2) = sqrt(8^2 + 4^2) = 8.9443 cm`

`AE = l_1 = sqrt(h_1^2 + r_2^2) = sqrt(5^2 + 2.5^2) = 5.5902 cm`

`pir^2 = pi*4^2 = 50.2655 cm^2`

`pir_2^2 = pi*2.5^2 = 19.635 cm^2`

`pirl= pi* 4 * 8.9443 = 112.3974 cm^2`

`pir_2l_1 = pi* 2.5 * 5.5902 = 43.9053 cm^2`

Total surface area = `(pir^2 + pir_1^2 + pi.r.l - pi.r_2.l_1)`

`T S A = 50.2655 + 19.635 + 112.3974 - 43.9053 =`138.3926 `cm^2`