A cone has a height of #6 cm# and its base has a radius of #4 cm#. If the cone is horizontally cut into two segments #3 cm# from the base, what would the surface area of the bottom segment be?

1 Answer
Oct 18, 2016

Total surface area of bottom segment is #130.80(2dp)#sq.cm

Explanation:

The cone is cut at 3 cm from base, So upper radius of the frustum of cone is #r_2=(6-3)/6*4=2 cm# ; slant ht #l=sqrt(3^2+(4-2)^2)=sqrt(9+4)=sqrt 13=3.606 cm#

Top surface area #A_t=pi*2^2=12.566 cm^2#
Bottom surface area #A_b=pi*4^2=50.265 cm^2#
Slant Area #A_s=pi*l*(r_1+r_2)=pi*3.606*(4+2)=67.971 cm^2#

Total surface area of bottom segment #=A_t+A_b+A_s=12.566+50.265+67.971=130.80(2dp)#sq.cm[Ans]