Subtraction and division problem: volume of 3 balls in cylinder

[zak100]

Homework Statement

Three identical balls fit snugly into a cylindrical can: the radius of spheres equals the radius of can, and the balls just touch the bottom and the top of the can,
If the formula for the volume of a sphere is
V = 4/3 PI * radius * radius * radius, what fraction of the volume of the can is taken up by the balls?

Homework Equations

Volume of sphere = 4/3 PI * r * r * r
Volume of cylinder = PI * r * r * h

The Attempt at a Solution

Suppose diameter of each ball is 2 so r = 1.

Vol of 3 balls = 3 * 4/3 PI * r * r *r = 4 * PI

Volume of cylinder = PI * r * r * h

Note h = 6 because 3 balls can fit in the cylinder

Volume of cylinder = 6 * PI
volume take up by balls is= 6* PI - 4 * PI = 2 PI

book is not doing subtraction.,
Some body please guide me why are we not doing subtraction.

Zulfi.

 

[berkeman]

Homework Statement

Three identical balls fit snugly into a cylindrical can: the radius of spheres equals the radius of can, and the balls just touch the bottom and the top of the can,
If the formula for the volume of a sphere is
V = 4/3 PI * radius * radius * radius, what fraction of the volume of the can is taken up by the balls?

Homework Equations

Volume of sphere = 4/3 PI * r * r * r
Volume of cylinder = PI * r * r * h

The Attempt at a Solution

Suppose diameter of each ball is 2 so r = 1.

Vol of 3 balls = 3 * 4/3 PI * r * r *r = 4 * PI

Volume of cylinder = PI * r * r * h

Note h = 6 because 3 balls can fit in the cylinder

Volume of cylinder = 6 * PI
volume take up by balls is= 6* PI - 4 * PI = 2 PI

book is not doing subtraction.,
Some body please guide me why are we not doing subtraction.

Zulfi.

The question is "what fraction of the volume", so you would use a ratio to get the answer, not a subtraction.

 

[zak100]

Hi,
Thanks. I was also thinking on those lines but you have removed my confusion.
Zulfi.