Question

The volume of a cylinder is 539 cm cube and the circumference of the base is 22 cm. find the height of the cylinder.

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Answer 1

Aproximated height is:

14 cm

Explanation:

volume of a cylinder = л r² h

л = 3.1416 (aprox)

r = radius

h = height

r = circunference/2л

r = 22/(2*3.1416)

r = 3.5 (aprox)

then volume is:

539 = 3.1416 * 3.5² * h

539 = 3.1416 * 12.25 * h

539 = 38.5 * h

h = 539/38.5

h = 14 cm (aprox)

Answer 2

13.994
`cm (5.sf)`

Explanation:

We know that the base of the cylinder is a circular base.

So circumference of base =
`2\pi r`

Given
`2\pi r=22cm\\\\r=(22)/(2\pi ) \\r=(11)/(\pi ) cm\\`

Volume of a cylinder =
`\pi r^(2) h` = 539
`cm^(3)`

Substitute r into the formula for volume of cylinder.

`\pi ((11)/(\pi ) )^(2) h=539\\\pi ((121)/(\pi ^(2) ) )h=539`

Now, we will cancel
`\pi` from the numerator and denominator.

`((121)/(\pi ) )h=539\\h = (539)/((121)/(\pi ) ) \\h = 539 * (\pi )/(121) \\h = 13.994cm(5s.f)`