A cone has a height of #11 cm# and its base has a radius of #5 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 · 2018-01-06T12:25:07

Total surface area of bottom segment is #193.86 # sq.cm.

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

of cone is #r_2=(11-2)/11*5~~4.09 # cm . Slant height is

#l=sqrt(2^2+(5-4.09)^2)=sqrt(4+0.83)=sqrt 4.83 ~~2.2# cm.

Top surface area #A_t=pi*4.09^2~~52.57# sq.cm

Bottom surface area #A_b=pi*5^2 ~~78.54# sq.cm

Slant Area #A_s=pi*l*(r_1+r_2)=pi*2.2*(5+4.09)~~62.74#

sq.cm. Total surface area of bottom segment is

#A_t+A_b+A_s=52.57+78.54+62.74 ~~193.86 (2dp)#

sq.cm [Ans]