Question

A cone has a height of `11 cm` and its base has a radius of `3 cm`. If the cone is horizontally cut into two segments `8 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

`:.color(purple)(=127.74cm^2`

Explanation:

:.Pythagoras: `c^2=11^2+3^2`

`:.c=L=sqrt(11^2+3^2)`

`:. c=Lcolor(purple)(=11.402cm`

`:.11/3=tan theta=3.666666667=74^@44’41.5”`

:.`color(purple)(S.A.` `= pi*r^2+pi*r*L`

:.S.A.`=3.141592654*3^2+pi*3*11.402`

:.S.A.`=28.274+107.461`

:.Total S.A.`color(purple)(=135.735cm^2`

`:.Cot 74^@44’41.5”*3=0.818cm=`radius of top part

:.Pythagoras: `c^2=3^2+0.818^2`

`:.c=L=sqrt(3^2+0.818^2)`

`:. c=Lcolor(purple)(=3.110cm` top part

:.S.A. top part`=pi*r^2+pi*r*L`

S.A. top part`:.3.141592654*0.818^2+pi*0.818*3.110`

S.A. top part`:.=2.102+7.992`

S.A. top part`:.color(purple)(=10.094cm^2`

:.S.A. Botom part`color(purple)(=135.735-10.094=125.641cm^2`

The total surface area of the bottom part got to include
the surface area of the circle of the top part.
:.S.A. Botom part:.=2.102+125.641=127.743 cm^2#

`:.color(purple)(=127.74cm^2` to the nearest 2 decimal places #