A cone has a height of #27 cm# and its base has a radius of #12 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?

1 Answer
Dec 4, 2017

Total surface area of bottom segment is #1086.15# sq.cm

Explanation:

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

frustum of cone is #r_2=(27-4)/27*12~~ 10.22(2dp)#cm.

Slant height #l=sqrt(4^2+(12-10.22)^2)=sqrt(16+3.17)#

#=sqrt 19.17 ~~4.38# cm

Top surface area #A_t=pi*10.22^2~~328.13#sq.cm

Bottom surface area #A_b=pi*12^2~~452.39# sq.cm

Slant Area #A_s=pi*l*(r_1+r_2)=pi*4.38*(12+10.22)#

# ~~305.62# sq.cm. Total surface area of bottom segment

is #T_(SA)=A_t+A_b+A_s=328.13+452.39+305.62#

#~~1086.15(2dp)# sq.cm[Ans]