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The curved surfaec area (c) of a cone is...

The curved surfaec area (c) of a cone is `pirl`, where `l=sqrt(r^(2)+h^(2))`, express h in terms of c and r.

A

`h=(1)/(pir)sqrt(c^(2)+pir^(2)r^(4))`

B

`h=(1)/(pir)sqrt(c-pir^(2)r^(2))`

C

`h=(1)/(pir)sqrt(c^(2)-pir^(2)r^(2))`

D

`h=(1)/(pir)sqrt(c+pir^(2)r^(4))`

Text Solution

Verified by Experts

The correct Answer is:
A
`c=pirl`
`(c)/(pir)=sqrt(r^(2)+h^(2))`
Squaring both sides,
`h^(2)=(c^(2))/(pi^(2)r^(2))-r^(2)`
`h^(2)=(c^(2)-pi^(2)r^(2))/(pir^(2)r^(2))`
`impliesh=sqrt((c^(2)-pi^(2)r^(4))/(pi^(2)r^(2)))=(1)/(rpi)sqrt(c^(2)-pi^(2)r^(4))`
`(thereforeh gt 0)`
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