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 #15 cm# from the base, what would the surface area of the bottom segment be?

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Answer 1 · 2018-01-09T11:31:29

Total surface area of bottom segment is #1435.60# sq.cm.

The cone is cut at 15 cm from base, So upper radius of the frustum

of cone is #r_2=((27-15)*12)/27~~ 5.33(2dp)#cm ; Slant ht

#l=sqrt(15^2+(12-5.33)^2)=sqrt(225+44.44)#

#=sqrt 269.44~~16.415# cm

Top surface area #A_t=pi*5.33^2 ~~89.36# sq.cm

Bottom surface area #A_b=pi*12^2~~452.389# sq.cm

Slant Area #A_s=pi*l*(r_1+r_2)=pi*16.415*(12+5.33)#

#~~893.854# sq.cm.

Total surface area of bottom segment is

#=A_t+A_b+A_s=89.36+452.389+893.854#

#~~1435.60(2dp)#sq.cm [Ans]