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?

1 Answer
Aug 25, 2016

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]