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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 $616 c m^{2} .$

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1078 c m^{3}

1000 c m^{3}

1070 c m^{3}

1008 c m^{3}

answer is A.

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Detailed Solution

Given,
Curved surface area: Total surface area=

1 : 2

Total surface area =

616 c m^{2}

Thus,

\frac{Curved surface area}{Total Surface area} = \frac{1}{2}

\frac{Curved surface area}{616} = \frac{1}{2}

Curved surface area = 308 \times 1

Curved surface area = 308 c m^{2}

Now, area of both bases,

2 π r^{2} = 616 - 308

2 π r^{2} = 308 c m^{2}

\Rightarrow 2 \times \frac{22}{7} r^{2} = 308

\Rightarrow r^{2} = \frac{308 \times 7}{2 \times 22}

\Rightarrow r^{2} = 49

\Rightarrow r^{2} = (7)^{2}

Thus,

r = 7 cm

If height is h and radius is r, then the curved surface area of cylinder is

2 πr h .

Thus,

∴ 2 πr h = 308 \Rightarrow 2 \times \frac{22}{7} r h = 308 \Rightarrow r h = \frac{308 \times 7}{2 \times 22}

\Rightarrow h = \frac{49}{7} . . . (i)

\Rightarrow h = 7 cm

So, the volume,

= π r^{2} h

= \frac{22}{7} \times 7 \times 7 \times 7

= 1078 c m^{3}

Hence, the correct Option is 1).

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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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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 $616 c m^{2} .$