Question

A cone has a height of `9 cm` and its base has a radius of `5 cm`. If the cone is horizontally cut into two segments `7 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

T S A = 236.1549

Explanation:

`OA = h = 9 cm, OB r = 5 cm, , AF = h_1 = 9-7 = 2 cm`

`FD = r_2 =( h_1 /h)*r = (2/ 9) * 5 = 1.1111 cm`

`AC = l = sqrt(h^2 + r^2) = sqrt(9^2 + 5^2) = 10.2956 cm`

`AE = l_1 = sqrt(h_1^2 + r_2^2) = sqrt(2^2 + 1.1111^2) = 2.2879 cm`

`pir^2 = pi*5^2 = 78.5398 cm^2`

`pir_2^2 = pi*1.1111^2 = 3.8784 cm^2`

#pirl= pi* 5 * 10.2956 = 161.7229 cm^2

#pir_2l_1 = pi* 1.1111 * 2.2879 = 7.9862 cm^2

Total surface area = `(pir^2 + pir_2^2 + pi.r.l - pi.r_2.l_1)`

T S A = 78.5398 + 3.8784 + 161.7229 - 7.9862 = 236.1549 `cm^2`