A cone has a height of #32 cm# and its base has a radius of #18 cm#. If the cone is horizontally cut into two segments #12 cm# from the base, what would the surface area of the bottom segment be?

1 Answer
Binayaka C.
Oct 11, 2016

Total surface area of bottom segment is #2680.67(2dp) cm^2#

Explanation:

The cone is cut at 12 cm from base, So upper radius of the frustum of cone is #r_2=(32-12)/32*18=11.25# cm ; slant ht #l=sqrt(12^2+(18-11.25)^2)=sqrt(144+45.56)=sqrt 189.56=13.77 cm#

Top surface area #A_t=pi*11.25^2=397.61 cm^2#
Bottom surface area #A_b=pi*18^2=1017.88 cm^2#
Slant Area #A_s=pi*l*(r_1+r_2)=pi*13.77*(18+11.25)=1265.18 cm^2#

Total surface area of bottom segment #=A_t+A_b+A_s=397.61+1017.88+1265.18=2680.67(2dp) cm^2#[Ans]

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