Firefighter Practice Exam

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What is the volume in liters of a cylinder that is 10 inches in height with a diameter of 4 inches?

2.5 liters
3.78 liters
1.5 liters
4.2 liters

The correct answer is: 3.78 liters

To find the volume of a cylinder, you can use the formula: \[ V = \pi r^2 h \] where $ V $ is the volume, $ r $ is the radius, and $ h $ is the height. First, the cylinder has a height of 10 inches and a diameter of 4 inches. To calculate the radius, you divide the diameter by 2: \[ r = \frac{4 \text{ inches}}{2} = 2 \text{ inches} \] Now, you can substitute the radius and height into the volume formula: \[ V = \pi (2 \text{ inches})^2 (10 \text{ inches}) \] \[ V = \pi (4 \text{ inches}^2) (10 \text{ inches}) \] \[ V = 40\pi \text{ cubic inches} \] Calculating the volume in cubic inches gives approximately: \[ V \approx 40 \times 3.14 \approx 125.6 \text{ cubic inches} \] Next, to convert cubic inches to liters, we use the conversion factor where 1 cubic inch is approximately 0.0163871 liters: