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Question
The area of the base of a conical solid is 38.5 cm2 and its volume is 154 cm3. Find the curved surface area of the solid.
Solution
Area of the base, πr2 = 38.5 cm2
Volume of the solid, V = 154 cm3
Curved surface area of the solid = πr2h
Volume, V `= 1/3 pir^2h`
`=> 154 = 1/3 pir^2h`
`=> h = (154 xx 3)/(pir^2)`
`=> h = (154 xx 3)/38.5`
= 12 cm
Area = 38.5
πr2 = 38.5
`=> r^2 = 38.5/3.14`
`=> r = sqrt(38.5/3.14)`
= 3.5
Curved surface area of solid = πrl
= `pirsqrt(r^2 + h^2)`
= `22/7 xx 3.5 xx sqrt(3.5^2 + 12^2)`
= `22/7 xx 3.5 xx 12.5`
= 137.5 cm2
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