Problem 709

Suppose that the height of the water in each container is $h$ cm.

Since the first container is a rectangular prism with a base that is 2 cm by 4 cm, then the volume of the water that it contains, in $\text{cm 3}$, is $2\times 4 \times h = 8h$.

Since the second container is a right cylinder with a radius of 1 cm, then the volume of the water that it contains, in $\text{cm 3}$, is $\pi \times 1^2 \times h = \pi h$.

Since the combined volume of the water is $\text{80 cm 3}$, then $8h + \pi h = 80$.

Thus, $h(8+\pi) = 80$ or $h = \dfrac{80}{8+\pi} \approx 7.18$.

Of the given answers, this is closest to $7.2$ (that is, the height of the water is closest to 7.2 cm).