Answer to Question #135820 in Physics for Christine Galbis

Question

a rectangular water tank has dimensions of 2.0 m x 1.0 m x 1.0 m. what would be the diameter of a 1.50-m high cylinder tank to contain the same amount of water that the rectangular tank contains?

Answer 1

The volume of water, that fits into rectangular tank is $V_r = 2 m \cdot 1 m \cdot 1 m = 2 m^3$.

Volume of cylinder is $V_c = \pi \left(\frac{d}{2}\right)^2 H$, where $d$ is diameter and $H$is height.

Hence, given volume of cylinder and height, the diameter must be $d = 2 \sqrt{\frac{V_c}{\pi H}}$. Replacing the volume of cylinder with the volume of rectangular tank, obtain: $d = 2 \sqrt{\frac{V_r}{\pi H}} \approx 1.3m$.