A can of tuna has a diameter of 4 inches and a height of 3 inches. What is the volume of the can of tuna? (Use 3.14 for π.) 56.52 in.3 150.72 in.3 113.04 in.3 37.68 in.3
The Correct Answer and Explanation is :
To calculate the volume of a cylinder, such as a can of tuna, we use the formula:
[
V = \pi r^2 h
]
where:
- (V) is the volume,
- (\pi) is approximately 3.14,
- (r) is the radius of the base, and
- (h) is the height of the cylinder.
Step 1: Find the radius
The diameter of the can is given as 4 inches. The radius ((r)) is half of the diameter:
[
r = \frac{\text{diameter}}{2} = \frac{4 \text{ in}}{2} = 2 \text{ in}
]
Step 2: Plug in the values
Now we have the radius and the height of the can, which is 3 inches. We can substitute these values into the volume formula:
[
V = \pi r^2 h = 3.14 \times (2 \text{ in})^2 \times 3 \text{ in}
]
Step 3: Calculate (r^2)
Calculating the radius squared:
[
r^2 = (2 \text{ in})^2 = 4 \text{ in}^2
]
Step 4: Substitute (r^2) into the volume formula
Now, we can substitute (r^2) back into the equation:
[
V = 3.14 \times 4 \text{ in}^2 \times 3 \text{ in}
]
Step 5: Multiply the values
First, multiply 4 by 3:
[
4 \text{ in}^2 \times 3 \text{ in} = 12 \text{ in}^3
]
Now substitute back into the volume formula:
[
V = 3.14 \times 12 \text{ in}^3
]
Step 6: Final calculation
Now multiply (3.14) by (12):
[
V = 37.68 \text{ in}^3
]
Conclusion
Thus, the volume of the can of tuna is 37.68 in³. This calculation illustrates how geometric formulas can be used to derive real-world quantities, such as the capacity of a container, which is essential in various applications, including cooking, food storage, and nutrition analysis. Understanding volume calculations is important not only for practical purposes but also for more complex scientific and engineering applications.