Question

A cone has a height of `15 cm` and its base has a radius of `9 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

Total Surface Area = 38.6979`cm^2`

Explanation:

`OA = h = 15 cm, OB r = 9 cm, , AF = h_1 = 15-7 = 8 cm`

`FD = r_2 =( h_1 /h)*r = (8/15)*9 = 24/5 cm`

`AC = l = sqrt(h^2 + r^2) = sqrt(15^2 + 9^2) = 17.4929`

`AE = l_1 = sqrt(h_1^2 + r_2^2) = sqrt(8^2 + (24/5)^2) = 9.33 cm`

`pir^2 = pi*9^2 = 254.469 cm^2`

`pir_2^2 = pi*(24/5)^2 = 72.3823 cm^2`

#pirl= pi917.4929 = 494.6 cm^2

`pir_2l_1 = pi* (25/4)* 9.33 = 183.1941`

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

`T S A = 254.469 + 72.823 + 494.6 - 183.1941 =**638.6979cm^2**`