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?

1 Answer
Binayaka C.
Jan 2, 2017

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]

Related questions
See all questions in Perimeter and Area of Non-Standard Shapes
Impact of this question
1170 views around the world
You can reuse this answer
Creative Commons License