Question

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?

Answer 1

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]