A cone has a height of #9 cm# and its base has a radius of #4 cm#. If the cone is horizontally cut into two segments #2 cm# from the base, what would the surface area of the bottom segment be?

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Answer 1 · 2018-02-13T12:39:51

Total surface area of bottom segment is #129.56# sq.cm.

The cone is cut at 2 cm from base, So upper radius of the frustum

of cone is #r_2=(9-2)/9*4=28/9~~ 3.11# cm. Slant height:

#l=sqrt(2^2+(4-3.11)^2)=sqrt(4+0.79)=sqrt 4.79~~2.19#

Top surface area #A_t=pi*3.11^2 ~~30.39 # 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*2.19*(4+3.11)~~48.9#

sq.cm. Total surface area of bottom segment is

#A=A_t+A_b+A_s=30.39+50.27+48.9=129.56 (2dp)#

sq.cm

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