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?

1 Answer
Binayaka C.
Jun 18, 2016

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]

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