# Find the height of a cylinder whose volume is 100 cm^3 and the circumference is 10 cm.

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We know that the volume of the cylinder is:

V = pi*r^2 * h (where r is the radius and h is the height)

100= pi*r^2*h

But we know that the circumference (c) = 10= 2*pi*r

==> r= 10/2*pi= 5/pi

Then:

100 = pi*(25/pi^2)*h

100= 25/pi ) h

==> h= 100*pi/25= 4*pi (pi=3.14)

==> h= 4(3.14) = 12.56 cm.

To find the height of a cylinder, having the data given by the enunciation, we'll have to calculate the volume of the cylinder.

V = h*pi*r^2, where pi*r^2 is the area of the base circle of the cylinder.

From this formula, we do not know the value of the radius, but we do know the value of the circumference of the circle:

L = 2*pi*r

10 = 2*pi*r

We'll divide by 2:

5 = pi*r

r = 5/pi

V = h*pi*r^2 = h*pi*(25/pi^2)

V = h * 25/pi

100 = h*25/pi

We'll divide by 25:

4 = h/pi

**h = 4*pi cm**

Given circumference , C = 10m and volume, V =100cm^3. To find the height h.

Solution:

Circumference is given by: C = 2pi*r ................................(1), where r is radius of cylinder. pi is a constant = 3.14159... of the circle.

Volume V is given by : V = pir^2*h................................(2)

Therefore,

From (1), r = C/(2pi) = 10/(2pi) = 1.59149431

From (2), h = V/(pi*r^2) = 100/(pi*1.59149431^2) = 12.56637061

The circumference and volume of a cylinder are given by the following formula:

Circumference = 2*pi*r

And

Volume = pi*r^2*h

Where: r = Radius of cylinder, and h = Height of cylinder.

Substituting given value of circumference in formula for circumference:

10 = 2*pi*r

r = 10/(2*pi) = 5/pi

Substituting this value of r and given value of volume in the formula for volume:

100 = pi*(5/pi)^2*h

100 = 25*h/pi

h = pi*100/25 = 4*pi = 4*3.14159 = 12.56636 cm

Answer:

Height of cylinder = 12.56536 cm