Question

A cone has a height of `24 cm` and its base has a radius of `5 cm`. If the cone is horizontally cut into two segments `16 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

The total surface area of the frustum of cone is `534.69` sq.cm.

Explanation:

The upper radius of frustum of cone is `16/24*5 =10/3`cm
The slant height of the frustum is obtained by applyin pythagorus theorem `l=(sqrt(16^2+(5-10/3)^2))=16.09 :.` Lateral area `= pi*l(r1+r2)= pi*16.09*(5+10/3)=pi*16.09*25/3 =421.24` sq.cm
Total surface area = Lateral area + bottom surface area + top surface area `SA= 421.24+pi.5^2+pi*(10/3)^2=421.24+78.54+34.91=534.69` sq.cm[Ans]