Question

A cone has a height of `4 cm` and its base has a radius of `6 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

Total surface area of the bottom segment = 69.1382

Explanation:

Refer diagram below :
`r = 3, r_2 = 3/2, h = 4, h_1 = 2,`
`l = sqrt(h^2+r^2) = sqrt(4^2+3^2) = 5`
`l_1 = sqrt(h_1^2 + r_2^2) = sqrt(2^2+2^2) = 2sqrt2`

Total surface area of the bottom segment
`= pir^2 + pir_2^2 + pirl - pir_2l_1`
`=pi3^2 + pi(3/2)^2 + pi*3*5 -pi*(3/2)*2sqrt2`
`= 9pi + (9/4)pi + 15pi - 3sqrt2*pi`
`69.1382 cm^2`