The diagram below shows a bin in the form of a frustum with square ends of sides 4cm and 10cm respectively. The height of the bin is 9 cm. Find the volume of the bin.

The side of the larger square end is $10 \text{ cm}$, so its area $A_1$ is:

$$A_1 = (10 \text{ cm})^2 = 100 \text{ cm}^2$$

The side of the smaller square end is $4 \text{ cm}$, so its area $A_2$ is:

$$A_2 = (4 \text{ cm})^2 = 16 \text{ cm}^2$$

The height $h$ is given as $9 \text{ cm}$.

$$V = 3 \text{ cm}(116 \text{ cm}^2 + \sqrt{1600 \text{ cm}^4})$$ $$V = 3 \text{ cm}(116 \text{ cm}^2 + 40 \text{ cm}^2)$$ $$V = 3 \text{ cm}(156 \text{ cm}^2)$$ $$V = 468 \text{ cm}^3$$

The volume of the bin is $468 \text{ cm}^3$.