Volume of a sphere vs volume of a cylinder?

Question

If there was a sphere enclosed in a cylinder (with a perfect fit), how much of the cylinder would be taken up by the sphere?

Thanks!

Answer 1

the volume of a sphere is (4/3) *pi *r^3 and the volume of a cylinder is

pi*r^2*h, note that the r's will have to be the same but also note that in order for the sphere to fit perfectly in the cylinder the height of the cylinder must be d =22r also so the volume of the cylinder becomes 2pi*r^3 so...look at the ratio of volume of the sphere to the cvolume of the cylinder (4/3) pi* r^3/2pi*r^3, the pi*r^3 cancel so you are left with the ratio of 4/3 to 2 or 4/3 divided by 2 which is 4/3 * 1/2 =4/6 = 2/3, so 2/3 of the cylinder is taken up by the sphere

Answer 2

Volume Of Sphere And Cylinder

Answer 3

Volume of a sphere is 4/3pir^3

volume of a cylinder is pir^2 h



If the sphere is a perfect fit then the height of the cylinder, h, will be the same as the diameter of the sphere, or radius * 2, so the volume of the cylinder will be pi r ^2 *(2r)

Take a random sphere with a radius of 2, the volume will be 33.5, if that was in a cylinder with perfect fit, the volume of the cylinder would be 50.26.

So a sphere with perfect fit in a cylinder would take up 66.6% of the cylinder.

Answer 4

start with two equations:



volume of a sphere: 4/3 (pi) r^3



four-thirds times pi times radius cubed



volume of a cylinder: pi r^2 h



pi times radius of the ends squared times height.



now if a sphere fits perfectly into a cylinder, then the height of the cylinder is 2r and the radius for the cylinder is the same as the radius of the sphere.



so first, find there volume of the cylinder and then find the volume of the sphere, then minus the volume of the sphere from the volume of the cylinder.



so if h = 2r



(pi)(r^2)(2r) - (4/3)(pi)(r^3) = your answer

Answer 5

you could just plug in some sample values into the equations for volume of a sphere vs volume of a cylinder

say you have a sphere with a 10 meter radius

volume of sphere= 4/3x3.14x5^3 = 523.6 m^3

volume of cylinder= 5^2x3.14x10 = 785 m^3

523.6/785= .666667 or 2/3rds

Answer 6

Sphere volume: (4/3)*(pi)*(r^3)

Cylinder volume: (pi)*(r^2)(2r) = 2(pi)*(r^3).



Therefore, the sphere takes up 2/3 of the cylinder.