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

Answer 1

Total surface area of bottom segment is `1500.5(1dp)` sq.cm

Explanation:

The cone is cut at 3 cm from base, So upper radius of the frustum of cone is `r_2=(12-3)/12*15=11.25`cm ; slant ht `l=sqrt(3^2+(15-11.25)^2)=sqrt(9+14.0625)=sqrt 23.0625=4.80`cm

Top surface area `A_t=pi*11.25^2=397.61` sq.cm
Bottom surface area `A_b=pi*15^2=706.858` sq.cm
Slant Area `A_s=pi*l*(r_1+r_2)=pi*4.80*(15+11.25)=396.03` sq.cm

Total surface area of bottom segment `=A_t+A_b+A_s=397.61+706.86+396.03=1500.5(1dp)`sq.cm[Ans]