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 #15 cm# from the base, what would the surface area of the bottom segment be?

1 Answer
Binayaka C.
Nov 16, 2016

Total surface area of bottom segment is #2795.38(2dp)# sq.cm.

Explanation:

The cone is cut at 15 cm from base, So upper radius of the frustum of cone is #r_2=(32-15)/32*18=9.5625#cm ; slant ht #l=sqrt(15^2+(18-9.5625)^2)=sqrt(225+71.19)=sqrt 296.19=17.21# cm.

Top surface area #A_t=pi*9.5625^2=287.27# sq.cm
Bottom surface area #A_b=pi*18^2=1017.88#sq.cm
Slant Area #A_s=pi*l*(r_1+r_2)=pi*17.21*(18+9.5625)=1490.23#sq.cm

Total surface area of bottom segment #=A_t+A_b+A_s=287.27+1017.88+1490.23=2795.38(2dp)#sq,cm[Ans]

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