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Vinayak Shenoy
Bunuel
Let right cylinder C have height h and radius r. Let both h and r be >2. If C has equal volume and surface area, what is h expressed in terms of r?

A. h=r
B. h=−r
C. h=1/(r−2)
D. h=rπ/(r−2)
E. h=2r/(r−2)


IMO E
volume of a cylinder = 2*pi*r*r*h
surface area= 2*pi*r*r+ 2*pi*r*h
Volume= surface area
2*pi*r*r*h= 2*pi*r(r+h)
solving we get h= 2r/(r-2)



Hi,
why is the volume of a cylinder = 2*pi*r*r*h and not just pi*r*r*h ?
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germanarmy
Vinayak Shenoy
Bunuel
Let right cylinder C have height h and radius r. Let both h and r be >2. If C has equal volume and surface area, what is h expressed in terms of r?

A. h=r
B. h=−r
C. h=1/(r−2)
D. h=rπ/(r−2)
E. h=2r/(r−2)


IMO E
volume of a cylinder = 2*pi*r*r*h
surface area= 2*pi*r*r+ 2*pi*r*h
Volume= surface area
2*pi*r*r*h= 2*pi*r(r+h)
solving we get h= 2r/(r-2)



Hi,
why is the volume of a cylinder = 2*pi*r*r*h and not just pi*r*r*h ?

Hi Germanarmy, you are right. I made a mistake. its pi*r*r*h. Solving this will give you the answer. I apologize :)
Thanks for correcting :)
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koenh
Vinayak Shenoy

2*pi*r*r*h= 2*pi*r(r+h)
solving we get h= 2r/(r-2)

Could you expand on how you solve this last part?

I corrected my mistake Koenh. its pi*r*r*h=2*pi*r(r+h)
solving this you get the answer.
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Vinayak Shenoy
koenh
Vinayak Shenoy

2*pi*r*r*h= 2*pi*r(r+h)
solving we get h= 2r/(r-2)

Could you expand on how you solve this last part?

I corrected my mistake Koenh. its pi*r*r*h=2*pi*r(r+h)
solving this you get the answer.

Thank you for your swift reply!
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