Given,
Total surface area of cylinder = 616 cm2
Ratio between curved surface area and total surface area of cylinder = 1 : 2
= \(\frac{2πrh}{2πr(h+r)}\) = \(\frac{1}{2}\)
= \(\frac{h}{h+r}\) = \(\frac{1}{2}\)
= 2h = h + r
= h = r
= 2πr(h + r) = 616 Given
= 2πr x 2r = 616(putting h = r)
= r2 = \(\frac{616}{4π}\) = \(\frac{616\times 7}{4\times 22}\) = 49
= r = \(\sqrt{49}\) = 7
Radius = 7 cm = height
∴ Volume of cylinder = πr2h = \(\frac{22}{7}\)x 7 x 7 x 7 = 1078 cm3