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in Surface Areas And Volumes by (56.3k points)

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.

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Best answer

We have,

Total surface area of cylinder = 616 cm2

Ratio between curved surface area and total surface area of cylinder = 1:2

2πrh / 2πr (h+r) = 1/2

h / (h+r) = 1/2

2h = h+r

h = r

We know, 2πr (h+r) = 616

2πr (r+r) = 616

2πr (2r) = 616

4πr2 = 616

r2 = 616/4π

= 616×7 / 4×22

= 4312 / 88

= 49

r = √49

= 7

Radius = 7cm

Height = 7cm

∴ Volume of cylinder = πr2h

= 22/7 × 7 × 7 × 7

= 1078 cm3

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