Question

A cone has a height of `14 cm` and its base has a radius of `8 cm`. If the cone is horizontally cut into two segments `5 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

T S A = 521.9289 `cm^2`

Explanation:

`OA = h = 14 cm, OB r = 8 cm, , AF = h_1 = 14-5 = 9 cm`

`FD = r_2 =( h_1 /h)*r = (9/ 14) * 8 = 5.1429 cm`

`AC = l = sqrt(h^2 + r^2) = sqrt(14^2 + 8^2) = 16.1245 cm`

`AE = l_1 = sqrt(h_1^2 + r_2^2) = sqrt(9^2 + 5.1429^2) = 10.3658 cm`

`pir^2 = pi*8^2 = 201.0619 cm^2`

`pir_2^2 = pi*5.1429^2 = 83.0933 cm^2`

#pirl= pi* 8 * 16.1245 = 405.2529 cm^2

#pir_2l_1 = pi* 5.1429 * 10.3658 = 167.4792 cm^2

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

T S A = 201.0619 + 83.0933 + 405.2529 - 167.4792 = 521.9289 `cm^2`