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If the ratio of the radius of the base to the height of a cylinder is 1 : 3 and the volume of the cylinder is $3234 cm 3,$ then its total surface area will be

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3089 cm 2

4629 cm 2

5490 cm 2

1232cm 2

answer is D.

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Detailed Solution

It is given that the ratio of the radius of the base to the height of a cylinder is 1 : 3 and the volume of the cylinder is

3234 cm 3 .

We know that the volume of a cylinder is

π r 2 h

and the total surface area of a cylinder is

2 π r h + r,

where r is the radius and h is the cylinder’s height.
Since the radius and height are in the ratio 1:3, let the radius be

x cm

and height be

3 x cm .

As the volume is given as

3234 cm 3,

we can calculate the value of

x

as given below:

Volume = 227 × x 2 × 3 x ⇒ 3234 = 227 × x 2 × 3 x ⇒ 3234 = 227 × 3 x 3 ⇒ x 3 = 3234 × 7 22 × 3

⇒ x 3 = 343 ⇒ x = 7 cm

Now, we can calculate the radius and height as,

x = 7 c m 3 x = 37 = 21 c m

Now, we know the value of height and radius, we can calculate the surface area as,
Question Image

Thus, the total surface area will be

1232 cm 2 .

Therefore the correct option is option (4).

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