Question

A cone has a height of `9 cm` and its base has a radius of `4 cm`. If the cone is horizontally cut into two segments `7 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

Total surface area of bottom segment is `170.4(1dp)` sq,cm

Explanation:

The cone is cut at 7 cm from base, So upper radius of the frustum of cone is `r_2=(9-7)/9*4=0.889`cm ; slant ht `l=sqrt(7^2+(4-0.889)^2)=sqrt(49+9.678)=sqrt 58.678=7.66 cm`
Top surface area `A_t=pi*0.889^2=2.48 cm^2`
Bottom surface area `A_b=pi*4^2=50.265 cm^2`
Slant Area `A_s=pi*l*(r_1+r_2)=pi*7.66*(4+0.889)=117.65 cm^2`

Total surface area of bottom segment `=A_t+A_b+A_s=2.48+50.265+117.65=170.4(1dp)`sq,cm[Ans]