A cone has a height of #5 cm# and its base has a radius of #4 cm#. If the cone is horizontally cut into two segments #1 cm# from the base, what would the surface area of the bottom segment be?

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Answer 1 · 2018-02-06T11:45:29

Total surface area of bottom segment is #111.4# sq.cm.

The cone is cut at #1# cm from base, So upper radius of the

frustum of cone is #r_2=(5-1)/5*4=16/5=3.2#cm ; slant ht:

#l=sqrt(1^2+(4-3.2)^2)=sqrt(1+0.64)=sqrt 1.64~~1.28# cm.

Top surface area #A_t=pi*3.2^2 ~~32.17 # sq.cm

Bottom surface area #A_b=pi*4^2~~50.27 # sq.cm

Slant Area #A_s=pi*l*(r_1+r_2)=pi*1.28*(4+3.2)~~28.97#

sq.cm.Total surface area of bottom segment is#A=A_t+A_b+A_s#

#=32.17+50.27+28.97~~ 111.4 (1dp)# sq.cm [Ans]