The ratio between the curved surface area and the total surface area

1.	The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Find the volume of the cylinder, if its total surface area is 616 cm2.
Answer» 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

The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Find the volume of the cylinder, if its total surface area is 616 cm2.

Answer»

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