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The sum of the radius of the base and height of a solid cylinder will be 37 cm. The total surface area of the solid cylinder is $1628 cm 2$ then what will be the volume of the cylinder?

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4600 m 3

4620 m 3

4622 m 3

4660 m 3

answer is B.

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Detailed Solution

Given that,
The sum of the radius of the base and the height of the cylinder is 37m.
The total surface area of the cylinder =

1628 m 2

The volume of the cylinder =

π r 2 h

The total surface area of the cylinder =

2 π r (r + h)

Here,
r = radius
h = height.
Substituting the values of the radius and height in the volume formula,

2 π r (r + h) = 1628 m 2 2 π r (37) = 1628

2 π r = 44 π r = 22 r = 7 m

height = 37-7 = 30m
The volume of the cylinder,

= 227 × 72 × 30 = 22 × 7 × 30 = 4620 m 3

Thus, the volume of the cylinder will be

4620 m 3

.
Therefore, the correct option is 2.

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