Question

A cone has a height of `16 cm` and its base has a radius of `6 cm`. If the cone is horizontally cut into two segments `7 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

Total surface area of bottom segment is `369.07.(2dp)cm^2`

Explanation:

The cone is cut at 7 cm from base, So upper radius of the frustum of cone is `r_2=(16-7)/16*6=3.375 cm` ; slant ht `l=sqrt(7^2+(6-3.375)^2)=sqrt(49+6.89)=sqrt 55.89=7.476 cm`
Top surface area `A_t=pi*3.375^2=35.785 cm^2`
Bottom surface area `A_b=pi*6^2=113.097 cm^2`
Slant Area `A_s=pi*l*(r_1+r_2)=pi*7.476*(6+3.375)=220.186 cm^2`
Total surface area of bottom segment `=A_t+A_b+A_s=35.785+113.097+220.186=369.07.(2dp)cm^2`[Ans]