Question

A cone has a height of `15 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 `167.47`sq.cm

Explanation:

The cone is cut at 4 cm from base, So upper radius of the frustum of cone is `r_2=(15-4)/15*4~~2.933` cm ;

slant ht `l=sqrt(4^2+(4-2.933)^2)=sqrt(16+1.138)=sqrt 17.138 ~~4.14(2dp) cm` .

Top surface area `A_t=pi*2.93^2=27.03` 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*4.14*(4+2.933)=90.17` sq.cm

Total surface area of bottom segment `=A_t+A_b+A_s=27.03+50.27+90.17 ~~167.47 (2dp)`sq.cm [Ans]