A cone has a height of #7 cm# and its base has a radius of #5 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
Sep 9, 2016

Total surface area of the bottom segment is #195.18 (2dp) sq.cm#

Explanation:

The cone is cut at 3 cm from base, So upper radius of the frustum of cone is #r_2=(7-3)/7*5=2.857#cm ; slant ht #l=sqrt(3^2+(5-2.857)^2)=sqrt(9+4.59)=3.69cm#
Top surface area #A_t=pi*2.857^2=25.64 sq.cm#
Bottom surface area #A_b=pi*5^2=78.54 sq cm#
Slant Area #A_s=pi*l*(r_1+r_2)=pi*3.69*(5+2.857)=91.00 sq cm#
Total surface area of bottom segment #=A_t+A_b+A_s=25.64+78.54+91.00=195.18 (2dp) sq.cm#[Ans]