Two balls fit into a circular can.

Question

Two balls fit into a circular can (See side-view below). What is the radius of each ball if the volume of the can is 100π cm^3?

Answer 1

Let radius of each ball is $r$ and of can is $R$. So from side view, $$\text{Width of can}=4r=2R\implies R=2r$$ Since volume of can is: $\text{Base area}\times\text{Height}$, $$(\pi R^2)(2r)=100\pi\implies R^2r=50\implies (4r^2)r=50$$ $$r=\sqrt[3]{12.5}\approx2.32$$

Answer 2

The volume of a cylinder (e.g. a can) is given by $V=\pi *r^2*h$. Now, the volume of a ball is given by $V=\frac{4}{3}\pi *r^3$.

Since we are given the volume of the can to be $100\pi$ cm$^3$, we may divide by $\pi$ to expression of both the radius and height. In this case, $r^2*h=100$. Now, since we have 2 balls in the can, one on top of the other, the radius of the ball is the same as the radius of the base of the can. This means that since there are 2 balls on top of each other, the height can be represented as $4*r=h$. Now we can substitute $h$ in terms of the radius and solve for $r$.