Question

A cone has a height of `12 cm` and its base has a radius of `15 cm`. If the cone is horizontally cut into two segments `10 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

Total surface area of bottom segment is `1606.57(2dp)`sq.cm

Explanation:

The cone is cut at 10 cm from base, So upper radius of the frustum of cone is `r_2=(12-10)/12*15=2.5`cm ; slant ht `l=sqrt(10^2+(15-2.5)^2)=sqrt(100+156.25)=sqrt 256.25=16.007`
Top surface area `A_t=pi*2.5^2=19.635`
Bottom surface area `A_b=pi*15^2=706.858`
Slant Area `A_s=pi*l*(r_1+r_2)=pi*16.007*(15+2.5)=880.075`
Total surface area of bottom segment `=A_t+A_b+A_s=19.635+706.858+880.075=1606.57(2dp)`sq,cm[Ans]