Problem 67 - Introductory and Intermediate Algebra for College Students 4th

Question

Two cylindrical cans of soup sell for the same price. One can has a diameter of 6 inches and a height of 5 inches. The other has a diameter of 5 inches and a height of 6 inches. Which can contains more soup and, therefore, is the better buy?

Step-by-Step Solution

Answer

After calculating and comparing the volumes of the two cans using the above steps, the can that has a larger calculated volume is the better buy as it contains more soup for the same price.

Step 1: Calculate the volume of the first can

Firstly, calculate the volume of the can with a diameter of 6 inches and a height of 5 inches. The radius is half of the diameter, which is 3 inches. Thus, using the formula \(V = \pi r^2h\), the volume of the first can becomes \(V_1 = \pi \cdot 3^2 \cdot 5\).

Step 2: Calculate the volume of the second can

Secondly, calculate the volume of the can with a diameter of 5 inches and a height of 6 inches. The radius in this case is half of the diameter, which is 2.5 inches. Thus, using the formula \(V = \pi r^2h\), the volume of the second can becomes \(V_2 = \pi \cdot 2.5^2 \cdot 6\).

Step 3: Compare the volumes

After calculating the volume of both cans, compare the two volumes. The can with the larger volume is the better buy as it contains more soup for the same price.