A cone has a height of #24 cm# and its base has a radius of #6 cm#. If the cone is horizontally cut into two segments #5 cm# from the base, what would the surface area of the bottom segment be?

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Answer 1 · 2017-09-19T12:21:45

Total surface area of bottom segment is 358.04 (2dp)# sq.cm.

The cone is cut at 5 cm from base, So upper radius of the frustum of

cone is #r_2=(24-5)/24*6=4.75#cm ; slant ht:

#l=sqrt(5^2+(6-4.75)^2)=sqrt(25+1.5625)=sqrt 26.5625=5.15#

Top surface area #A_t=pi*4.75^2=70.88 # sq.cm

Bottom surface area #A_b=pi*6^2=113.1 # sq.cm

Slant Area #A_s=pi*l*(r_1+r_2)=pi*5.15*(6+4.75)=174.06# sq.cm

Total surface area of bottom segment

#=A_t+A_b+A_s=70.88+113.1+174.06=358.04 (2dp)#

sq.cm [Ans]