A can of beans has a diameter of 8 inches and a height of 5 inches. What is the volume of the can? Use 3.14 for [tex]$\pi$[/tex]. Round to the nearest tenth.
Answer (2)
Calculate the radius using the diameter: r = 2 8 = 4 inches.
Apply the formula for the volume of a cylinder: V = π r 2 h .
Substitute the given values: V = 3.14 × ( 4 2 ) × 5 = 3.14 × 16 × 5 = 251.2 cubic inches.
State the final answer: 251.2 cubic inches.
Explanation
Problem Analysis We are given a cylindrical can of beans with a diameter of 8 inches and a height of 5 inches. We need to find the volume of the can, using 3.14 as the value for π , and round the answer to the nearest tenth.
Calculate the Radius First, we need to find the radius of the can. The radius is half of the diameter. So, we have: r = 2 d = 2 8 = 4 The radius of the can is 4 inches.
Calculate the Volume Now, we can use the formula for the volume of a cylinder, which is V = π r 2 h . We are given that h = 5 inches and we calculated that r = 4 inches. We are also given that we should use 3.14 for π . Plugging these values into the formula, we get: V = 3.14 × ( 4 2 ) × 5 V = 3.14 × 16 × 5 V = 3.14 × 80 V = 251.2 The volume of the can is 251.2 cubic inches.
Final Answer Since the volume is already given to the nearest tenth, we don't need to round it. The volume of the can of beans is 251.2 cubic inches.
Examples
Understanding the volume of cylinders is useful in many real-world scenarios. For example, when designing storage tanks for liquids or gases, engineers need to accurately calculate the volume to ensure the tank meets the required capacity. Similarly, in packaging and manufacturing, knowing the volume of containers helps optimize material usage and transportation costs. Even in cooking, understanding volume helps in scaling recipes and choosing the right size cookware.
The volume of the cylindrical can is calculated using the formula for the volume of a cylinder. By measuring the radius and height, we find the volume to be 251.2 cubic inches. This answer is already rounded to the nearest tenth as required.
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