Question

A cone has a height of `24 cm` and its base has a radius of `8 cm`. If the cone is horizontally cut into two segments `15 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

`:.color(purple)(=747.46cm^2` to the nearest `cm^2`

Explanation:

:.Pythagoras: `c^2=24^2+8^2`

`:.c=L=sqrt(24^2+8^2)`

`:. c=Lcolor(purple)(=25.298cm`

`:.24/8=tan theta=3.0=71^@33’54”`

:.`color(purple)(S.A.`= pir^2+pir*L#

:.S.A.`=3.141592654*8^2+pi*8*25.298`

:.S.A.`=201.062+635.808`

:.Total S.A.`color(purple)(=836.870cm^2`

`:.Cot 71^@33’54”*9=3.0cm=`radius of top part

:.Pythagoras: `c^2=9^2+3.0^2`

`:.c=L=sqrt(9^2+3.0^2)`

`:. c=Lcolor(purple)(=9.487cm` top part

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

S.A. top part`:.3.141592654*3.0^2+pi*3.0*9.487`

S.A. top part`:.=28.274+89.413`

S.A. top part`:.color(purple)(=117.687cm^2`

:.S.A. Botom part`color(purple)(=836.870-117.687=719.183cm^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:.=28.274+719.183=747.457 cm^2#

`:.color(purple)(=747.46cm^2` to the nearest 2 decimal places #