Question

A cone has a height of `8 cm` and its base has a radius of `4 cm`. If the cone is horizontally cut into two segments `4 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

Total surface area of bottom segment is `147.13 (2 dp)` sq.cm

Explanation:

The cone is cut at `4` cm from base, So upper radius of the

frustum of cone is `r_2=(8-4)/8*4=2` cm ;

Slant height: `l=sqrt(4^2+(4-2)^2)=sqrt20 ~~ 4.47` cm

Top surface area `A_t=pi*2^2~~ 12.57` sq.cm

Bottom surface area `A_b=pi*4^2~~50.27` sq.cm

Slant Area `A_s=pi*l*(r_1+r_2)=pi*4.47*(4+2)`

`~~84.3` sq.cm

Total surface area of bottom segment is ,

`A=A_t+A_b+A_s=12.57+50.27+84.3~~147.13 (2dp)`

sq.cm. [Ans]