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The ratio between the radius of the base and the height of a cylinder is 2: 3 .Find the total surface area of the cylinder, if its volume is $1617 cm 3$ .

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760

c m 2

780

c m 2

750

c m 2

770

c m 2

answer is D.

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Detailed Solution

It is given the ratio between the radius of the base and height of cylinder is 2:3 and its volume is

1617 cm 3

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

2 π r h + r

.
The volume of the cylinder is

π r 2 h

.
The ratio between the radius of the base and the height of a cylinder is

2 : 3

.
Let r be the radius of the base of the cylinder and

h

be the height of the cylinder.
So,

r : h = 2 : 3

⇒ r h = 23

⇒ r = 23 h

… … (1)

Find the value of the radius and height of the cylinder.
Since, the volume of the cylinder is

1617 c m 3

So,

πr 2 h=1617cm 3

……(2)
Put (1) in (2),

π × 23 h 2 × h = 1617

⇒ 227 × 49 h 2 × h = 1617

⇒ 8863 h 3 = 1617

⇒ h 3 = 92618

⇒ h 3 = 2123

⇒ h = 212 c m

So, height of cylinder (h) is

212 c m

.
Radius of cylinder (r) is,

r = 23 h ⇒ r = 23 × 212 ⇒ r = 7 c m

The total surface area of the cylinder is

2 π r h + r

T . S . A . = 2 π r h + r ⇒ T . S . A . = 2 × 227 × 7 212 + 7

⇒ T . S . A . = 44 × 21 + 14 2

⇒ T . S . A . = 44 × 35 2

⇒ T . S . A . = 770 c m 2

Therefore, the total surface area of the cylinder is 770

c m 2

.
Hence option (4) is correct.

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