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Question
From a solid right circular cylinder of height 2.4 cm and radius 0.7 cm, a right circular cone of same height and same radius is cut out. Find the total surface area of the remaining solid.
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Solution
Given that,
Height (h) of the conical part = Height (h) of the cylindrical part = 2.4 cm
Radius (r) of the cylindrical part = 0.7 cm
Slant height (l) of conical part = `sqrt(r^2 + h^2)`
= `sqrt((0.7)^2 + (2.4)^2) = sqrt(0.49 + 5.76)`
`= sqrt(6.25) = 2.5`
Total surfece area of the remaining soild will be
= CSA of cylindrical part + CSA of conical part + Area of cylindrical base
`= 2pirh + pirl + pir^2`
`= 2 xx 22/7 xx 0.7 xx 2.4 + 22/7 xx 0.7 xx 2.5 + 22/7 xx 0.7 xx 0.7`
= 4.4 x 2.4 + 2.2 xx 2.5 + 2.2 xx 0.7
= 10.56 + 5.50 + 1.54 = 17.60 cm2
The total surface area of the remaining solid is 17.60 cm2
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