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

1 Answer
Jun 28, 2017

Total surface area of bottom segment is #167.47#sq.cm

Explanation:

The cone is cut at 4 cm from base, So upper radius of the frustum of cone is #r_2=(15-4)/15*4~~2.933 # cm ;

slant ht #l=sqrt(4^2+(4-2.933)^2)=sqrt(16+1.138)=sqrt 17.138 ~~4.14(2dp) cm # .

Top surface area #A_t=pi*2.93^2=27.03# 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*4.14*(4+2.933)=90.17# sq.cm

Total surface area of bottom segment #=A_t+A_b+A_s=27.03+50.27+90.17 ~~167.47 (2dp)#sq.cm [Ans]