A cone has a height of #24 cm# and its base has a radius of #8 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
Dec 12, 2017

Total surface area of bottom segment is #504.02 (2dp)# sq.cm

Explanation:

The cone is cut at 3 cm from base, So upper radius of the frustum

of cone is #r_2=(24-3)/24*8=7 # cm ;

Slant ht: #l=sqrt(3^2+(8-7)^2)=sqrt(9+1)=sqrt 10~~3.16# cm.

Top surface area #A_t=pi*7^2 ~~153.94 # sq.cm

Bottom surface area #A_b=pi*8^2~~201.06 # sq.cm

Slant Area #A_s=pi*l*(r_1+r_2)=pi*3.16*(8+7)~~149.02# sq.cm.

Total surface area of bottom segment is

#=A_t+A_b+A_s=153.94+201.06.1+149.02~~504.02 (2dp)#

sq.cm [Ans]