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A semi circular sheet with area 154 sq unit to used to from a cone without cotting the sheet. find the volume of cone thus formed.



let radius of cone be =R
Height of cone=h
slant length=s

Then the curve area of cone =πRs
we know s=r
Area of semicircle  πr²/2=πRs
                                  ⇒ πs²=2πRs
                                  ⇒   2R=s

We have h= √(s²-R²)=√3*R

From question πRs= 2πR²=154
                      R²=24.509 ⇒R=4.950
    Then h=√3*R= 8.574

Volume of cone=πR²h/3=220.082
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