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 `1 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

Total surface area of bottom segment is `172.09(2dp)`sq.cm

Explanation:

The cone is cut at 1 cm from base, So upper radius of the frustum of cone is `r_2=(7-1)/7*5=30/7~~4.286`cm ; slant ht `l~~sqrt(1^2+(5-4.29)^2)~~1.23`

Top surface area `A_t=pi*4.286^2~~57.70` 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*1.23*(5+4.285)=35.85` sq.cm

Total surface area of bottom segment `=A_t+A_b+A_s~~57.70+78.54+35.85 ~~172.09(2dp)`sq.cm[Ans]