Question

A cone has a height of `14 cm` and its base has a radius of `7 cm`. If the cone is horizontally cut into two segments `6 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

`T S A = 436.2322 cm^2`

Explanation:

`OA = h = 14 cm, OB r = 7 cm, , AF = h_1 = 8 cm`

`FD = r_2 =( h_1 /h)*r = (8 / 14) * 7 = 4 cm`

`AC = l = sqrt(h^2 + r^2) = sqrt(14^2 + 7^2) = 15.6525`

`AE = l_1 = sqrt(h_1^2 + r_2^2) = sqrt(8^2 + 4^2) = 8.9443 cm`

`pir^2 = pi*7^2 = 154 cm^2`

`pir_2^2 = pi*4^2 = 50.2655 cm^2`

#pirl= pi* 7 * 15.6525 = 344.355cm^2

#pir_2l_1 = pi* 4 * 8.9443 = 112.3973 cm^2

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

`T S A = 154 + 50.2655 + 344.355 - 112.3973 = 436.2232 cm^2**`