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

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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

 

 

krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

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

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