Find the area of the base of a rectangular prism if its volume is \( 350 \mathrm{~cm}^{3} \) and its height is 5 cm .

To find the area of the base of a rectangular prism, you can use the formula for the volume of a prism, which is given by: \[ \text{Volume} = \text{Base Area} \times \text{Height} \] In this case, you know the volume is \( 350 \mathrm{~cm}^{3} \) and the height is \( 5 \mathrm{~cm} \). To find the base area, rearrange the formula: \[ \text{Base Area} = \frac{\text{Volume}}{\text{Height}} = \frac{350 \mathrm{~cm}^{3}}{5 \mathrm{~cm}} = 70 \mathrm{~cm}^{2} \] So, the area of the base of the rectangular prism is \( 70 \mathrm{~cm}^{2} \). Talking about prisms, did you know that the concept of volume has been around since ancient times? Ancient Egyptians were among the first to study the volumes of geometric shapes, applying their knowledge for practical purposes like storage and construction! They even created specialized tools, leveraging geometry to stack their massive stones perfectly. Now, as you venture into the world of shapes and volumes, remember that making a quick sketch can really help visualize your problems. Sometimes, when dealing with more complex shapes, we might forget dimensions or the relationship between them. Drawing a simple diagram can quickly clarify what you need to calculate, aiding your understanding and reducing mistakes!