A cone has a height of #6 cm# and its base has a radius of #2 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 · 2017-10-21T12:16:14

Total surface area of bottom segment is #51.55# sq.cm.

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

frustum of cone is #r_2=(6-5)/6*2=1/3 =0.33#cm ;

Slant height of the frustum of cone is

#l=sqrt(5^2+(2-1/3)^2)=sqrt(25+2.78)~~5.27# cm

Top surface area #A_t=pi*0.33^2 ~~0.35 # sq.cm

Bottom surface area #A_b=pi*2^2=12.57 # sq.cm

Slant Area #A_s=pi*l*(r_1+r_2)=pi*5.27*(2+0.33)~~38.63# sq.cm

Total surface area of bottom segment is

#=A_t+A_b+A_s=0.35+12.57+38.63 ~~51.55 (2dp)#

sq.cm [Ans]