Solve

Guides

0

Question

- r=(100π)1/3,h=5(100π)1/3
- r=(500π)1/3=h
- r=(1000π)1/3,h=(125π)1/3
- r=(20π)1/3,h=(100π)1/3

Open in App

Solution

Verified by Toppr

Let r and h be the internal radius and height of the cylindrical vessel and let V denote the volume of the material.

Now, V=πr2h

⇒500=πr2h

⇒h=500πr2 ...(1)

Now, S=(2πrh+πr2)2100 (As 2100 is thickness)

=(1000r+πr2).150

For maximum or minimum ,

dsdr=(−1000r2+2πr)150=0

⇒πr3=500

∴πr3=500=V=πr2h

or r=(500π)1/3=h

Clearlyd2Sdr2=(4Vr3+2π).150=+ive

∴ For minimum volume, r=(500π)1/3=h

Was this answer helpful?

0