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.
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let radius of cone be =R
height of cone=h
slant length=s
Then the curve area of cone =πR s
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 cm²
height of cone=h
slant length=s
Then the curve area of cone =πR s
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 cm²
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