Question

You want to buy a pickup truck and are interested in one with a large carrying capacity. One model features a rectangular prism-shaped cargo space, measuring 6 feet by 10 feet by 2 feet; another has a space with dimensions 5 feet by 11 feet by 3 feet. Which truck provides you with the most carrying capacity (that is, the most volume)? Explain.

Short answer

Answer: The second truck provides the most carrying capacity with a cargo space volume of 165 cubic feet, compared to the first truck's volume of 120 cubic feet. The difference in their carrying capacities is 45 cubic feet (165 cubic feet - 120 cubic feet).

Step-by-step solution

Write down the dimensions of both cargo spaces

For the first truck, the cargo space dimensions are 6 feet by 10 feet by 2 feet. For the second truck, the cargo space dimensions are 5 feet by 11 feet by 3 feet.

Recall the formula to calculate the volume of a rectangular prism

The volume \(V\) of a rectangular prism is calculated by: \(V = l × w × h\) where \(l\) is the length, \(w\) is the width, and \(h\) is the height.

Calculate the volume of the first truck's cargo space

Using the formula and the dimensions (6 feet, 10 feet, and 2 feet), we calculate the volume of the first truck's cargo space: \(V_1 = 6 × 10 × 2\) \(V_1 = 120~ft^3\)

Calculate the volume of the second truck's cargo space

Using the formula and the dimensions (5 feet, 11 feet, and 3 feet), we calculate the volume of the second truck's cargo space: \(V_2 = 5 × 11 × 3\) \(V_2 = 165~ft^3\)

Compare the volumes and determine the truck with the most carrying capacity

Comparing the volumes \(V_1\) and \(V_2\), we see that: \(165~ft^3 > 120~ft^3\) So, the second truck provides more carrying capacity because it has a higher volume for its cargo space (165 cubic feet) compared to the first truck (120 cubic feet).