Question

A cone has a height of `7 cm` and its base has a radius of `5 cm`. If the cone is horizontally cut into two segments `2 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

T S A = 184.7937

Explanation:

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

`FD = r_2 =( h_1 /h)*r = (5/ 7) * 5 = 3.5714 cm`

`AC = l = sqrt(h^2 + r^2) = sqrt(7^2 + 5^2) = 8.6023 cm`

`AE = l_1 = sqrt(h_1^2 + r_2^2) = sqrt(5^2 + 3.5715^2) = 6.1446 cm`

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

`pir_2^2 = pi*3.5715^2 = 40.0729 cm^2`

`pirl= pi* 5 * 8.6023 = 135.1246 cm^2`

`pir_2l_1 = pi* 3.5715 * 6.1446 = 68.9436 cm^2`

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

`T S A = 78.5398 + 40.0729 + 135.1246 - 68.9436 =`184.7937 `cm^2`