The question is incomplete. The complete question is :
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 54 meters cubed. Amie found the volume of the sphere. A sphere with height h and radius r. A cylinder with height h and radius r. Her work is shown below. V = two-thirds + 54. V = two-thirds + StartFraction 162 Over 3 EndFraction. V = StartFraction 164 Over 3 EndFraction meter cubed. What is Amie's error?
Solution :
Amie should have multiplied 54 by two-thirds.
Given that sphere and the cylinder have the same radius as well as same height. The volume of the cylinder is 54 inch cube.
Volume of the sphere =
.......... (i)
Volume of cylinder =
....................(ii)
Therefore, the ratio of sphere volume to cylinder volume is,
......(iii)
Divide both the sides by
, we get
..........(iv)
We know that the height of the sphere = diameter of the sphere
The diameter of the sphere is D = 2r
Also the sphere height = cylinder height
So, the height of the cylinder = 2r
Therefore, substituting the height of the cylinder as 2r that is represented as h in equation (iv) is given by :
.............(v)
Now dividing both the sides by 2r, we get
..................(vi)
Thus for equation (vi), we see, sphere volume =
of the cylinder volume
∴ sphere volume =

= 36 meter cube
Thus, Amie should have multiplied 54 by
.