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The volume and the curved surface area of cylinder are $1650 cm 3$ and $660 cm 2$ respectively. Find the radius and height of the cylinder respectively.

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1cm, 7cm

12cm, 23cm

4cm, 54cm

5cm, 21cm

answer is D.

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Detailed Solution

It is given volume and curved surface area of cylinder are

1650 cm 3

and

660 cm 2

.
Curved surface area =

2 π r h

Volume =

π r 2 h

So,

π r 2 h = 1650

…… (1)
And

2 π r h = 660

……(2)
Dividing (1) by (2),

π r 2 h 2 π r h = 1650660

⇒ r 2 = 52

⇒ r = 5 c m

Thus, the radius of the base of cylinder =

5 cm

Substitute the value of

r

2

2 π × 5 h = 660

⇒ 2 × 227 × 5 × h = 660

⇒ 2207 × h = 660

⇒ h = 21

cm
Thus, the height of the cylinder =

21 cm

Therefore, the radius and height of the cylinder are

5 cm

and

21 cm

respectively.
Hence option (4) is correct.

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