Question

which figure has a greater volume and by how much? the volume of figure 1 is 120 cm³ greater than the volume of figure 2. the volume of figure 1 is 45 cm³ greater than the volume of figure 2. the volume of figure 2 is 120 cm³ greater than the volume of figure 1. the volume of figure 2 is 45 cm³ greater than the volume of figure 1.

Explanation:

Step1: Calculate volume of Figure 1

Volume of rectangular part: \(15\times6\times5 = 450\ \text{cm}^3\)
Volume of triangular - prism part: \(\frac{1}{2}\times15\times6\times3=135\ \text{cm}^3\)
Total volume of Figure 1: \(450 + 135=585\ \text{cm}^3\)

Step2: Calculate volume of Figure 2

Volume of rectangular part: \(15\times6\times5 = 450\ \text{cm}^3\)
Volume of pyramid part: \(\frac{1}{3}\times15\times6\times3 = 90\ \text{cm}^3\)
Total volume of Figure 2: \(450+90 = 540\ \text{cm}^3\)

Step3: Find the difference

Difference in volumes: \(585 - 540=45\ \text{cm}^3\)

Answer:

The volume of figure 1 is \(45\ \text{cm}^3\) greater than the volume of figure 2.