Question

A cone has a height of `24 cm` and its base has a radius of `6 cm`. If the cone is horizontally cut into two segments `9 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

`T S A = **529.738cm^2**`

Explanation:

`OA = h = 24 cm, OB r = 6 cm, , AF = h_1 = 9 cm`

`FD = r_2 =( h_1 /h)*r = (9/ 24) * 6 = 2.25 cm`

`AC = l = sqrt(h^2 + r^2) = sqrt(24^2 + 6^2) = 24.7386 cm`

`AE = l_1 = sqrt(h_1^2 + r_2^2) = sqrt(9^2 + 2.25^2) = 9.277 cm`

`pir^2 = pi*6^2 = 113.0973 cm^2`

`pir_2^2 = pi*2.25^2 = 15.9043 cm^2`

#pirl= pi* 6 * 24.7386 = 466.3116 cm^2

#pir_2l_1 = pi* 2.25 * 9.277 = 65.5752 cm^2

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

`T S A = 113.0973 + 15.9043 + 466.3116 - 65.5752 = **529.738 cm^2**`