Two cylindrical tanks sit side by side on a level surface. The first tank has a radius of 4 metres, a height of 10 metres, and is full of water. The second tank has a radius of 6 metres, a height of 8 metres, and is empty. Water is pumped from the first tank to the second until the depth of water in both tanks is the same. The depth of water in each tank, in metres, is
(A) 4
(B) 5
(C) $\frac{46}{15}$
(D) $\frac{52}{17}$
(E) $\frac{40}{13}$

## Part C: Each correct answer is worth 8.
Let the final depth of the water be $h$.

The total initial volume of water is

$\pi(4 \mathrm{~m})^{2}(10 \mathrm{~m})=160 \pi \mathrm{m}^{3}$.

When the depths of water are equal, $\pi(4 \mathrm{~m})^{2} h+\pi(6 \mathrm{~m})^{2} h=160 \pi \mathrm{m}^{3}$

$$
\begin{aligned}
\left(52 \pi \mathrm{m}^{2}\right) h & =160 \pi \mathrm{m}^{3} \\
h & =\frac{160}{52} \mathrm{~m} \\
h & =\frac{40}{13} \mathrm{~m}
\end{aligned}
$$

![](https://cdn.mathpix.com/cropped/2024_04_20_688a3b42f69739f2e244g-234.jpg?height=385&width=502&top_left_y=623&top_left_x=1321)

ANSWER: (E)