A cone has a height of #15 cm# and its base has a radius of #4 cm#. If the cone is horizontally cut into two segments #10 cm# from the base, what would the surface area of the bottom segment be?

1 Answer
Binayaka C.
Dec 8, 2016

Total surface area of bottom segment is #229.26(2dp)#sq.cm

Explanation:

The cone is cut at 10 cm from base, So upper radius of the frustum of cone is #r_2=(15-10)/15*4=1.333# cm ; slant ht #l=sqrt(10^2+(4-1.33)^2)=sqrt(100+7.11)=sqrt 107.11=10.349#cm.

Top surface area #A_t=pi*1.33^2=5.585# sq.cm
Bottom surface area #A_b=pi*4^2=50.265# sq.cm
Slant Area #A_s=pi*l*(r_1+r_2)=pi*10.349*(4+1.33)=173.406# sq.cm

Total surface area of bottom segment #=A_t+A_b+A_s=5.585+50.265+173.406=229.26(2dp)#sq.cm[Ans]

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