A company makes steel rods shaped like cylinders. Each rod has a radius of 4 centimeters and a height of 30 centimeters. How much steel will the company need to make 113 rods? Use 3.14 for \( \pi \), and do not round your answer.

To calculate the volume of one steel rod, we use the formula for the volume of a cylinder: \( V = \pi r^2 h \). Here, \( r \) is the radius (4 cm) and \( h \) is the height (30 cm). Plugging in the numbers: \( V = 3.14 \times (4^2) \times 30 = 3.14 \times 16 \times 30 = 1507.2 \text{ cm}^3 \). To find the total volume for 113 rods, simply multiply the volume of one rod by 113: \( 1507.2 \text{ cm}^3 \times 113 = 170,817.6 \text{ cm}^3 \). So, the company will need 170,817.6 cubic centimeters of steel to produce 113 rods. Steel rods, being vital in construction and industry, play significant roles in structural integrity. For instance, they are commonly used in reinforced concrete which allows buildings to withstand heavy loads and earthquake forces. The strength of steel helps ensure safety and durability, making it a go-to material for engineers and builders around the globe. When calculating volumes like this, it’s crucial to keep track of your units and ensure you’re using the correct values for π. A common mistake is forgetting to square the radius or mistakenly changing units, leading to incorrect volume calculations. Always double-check your substitutions and calculations, especially in multi-step problems!