A cone has a height of #12 cm# and its base has a radius of #4 cm#. If the cone is horizontally cut into two segments #6 cm# from the base, what would the surface area of the bottom segment be?

1 Answer
Sep 18, 2016

Total surface area of bottom segment is #182.05(2dp)# sq,cm

Explanation:

The cone is cut at 6 cm from base, So upper radius of the frustum of cone is #r_2=(12-6)/12*4=2.0# cm ; slant ht #l=sqrt(6^2+(4-2.0)^2)=sqrt(36+4)=sqrt 40.0=6.325 cm#
Top surface area #A_t=pi*2.0^2=12.566#
Bottom surface area #A_b=pi*4^2=50.265#
Slant Area #A_s=pi*l*(r_1+r_2)=pi*6.325*(4+2)=119.223#
Total surface area of bottom segment #=A_t+A_b+A_s=12.566+50.265+119.223=182.05(2dp)#sq,cm[Ans]