A solid cylinder has a total surface area of 231 cm2. Its curved surface area is 23 of the total surface area. Find the volume of the cylinder..
Let the radius of the cylinder be r and the height be h.
The curved surface area of the cylinder is given by
2πrh
Total surface area of the solid cylinder is given as the sum of the curved surface area and the areas of the base and the top:
2πr2+2πrh
Given that
2πrh=23(2πrh+2πr2)
⇒h=2r
Also, given that
i.e
2πr2+2πr.2r=231
6πr2=231
⇒r=√772π
Volume of the cylinder:
=πr2h
=πr2.2r=2πr3
=2π(772π)3/2
=77√772π
Hence, volume of the cylinder =77√772π cm3