Question

A cone has a height of `35 cm` and its base has a radius of `15 cm`. If the cone is horizontally cut into two segments `24 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

Total surface area of bottom segment is `2393.31 cm^2`

Explanation:

The cone is cut at 24 cm from base, So upper radius of the frustum of cone is `r_2/15=(35-24)/35or r_2=11*15/35=33/7=4.71`cm ; slant ht `l=sqrt(24^2+(15-4.71)^2)=sqrt(576+105.88)=26.11 cm`
Top surface area `A_t=pi*4.71^2=69.69 cm^2`
Bottom surface area `A_b=pi*15^2=706.86 cm^2`
Slant Area `A_s=pi*l*(r_1+r_2)=pi*26.11*(15+4.71)=1616.76 cm^2`
Total surface area of bottom segment `=A_t+A_b+A_s=69.69+706.86+1616.76=2393.31(2dp) cm^2`[Ans]