A prism and a pyramid have the same base and the same height. Find the ratio of the volumes of the prism and the pyramid.

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**Solution:**

1. The volume of a prism is given by:
   $$V_{prism} = B 	imes h$$
   where *B* is the area of the base and *h* is the height.

2. The volume of a pyramid is given by:
   $$V_{pyramid} = \frac{1}{3} 	imes B 	imes h$$

3. Since both have the same base and height, the ratio of their volumes is:
   $$\frac{V_{prism}}{V_{pyramid}} = \frac{B 	imes h}{\frac{1}{3} 	imes B 	imes h}$$

4. Canceling *B* and *h* from numerator and denominator:
   $$\frac{V_{prism}}{V_{pyramid}} = \frac{1}{\frac{1}{3}} = 3$$

5. Therefore, the ratio of volumes is:
   $$V_{prism} : V_{pyramid} = 3 : 1$$

**Answer:** 3:1

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