High School Placement Test (HSPT) Practice Test

What is the volume of a cylinder with a diameter of 3 mm and a height of 7 mm?

1. 28.27

2. 49.48

3. 78.54

4. 14.14

The correct answer is: 49.48

To find the volume of a cylinder, we use the formula: \[ V = \pi r^2 h \] where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height of the cylinder. First, we need to determine the radius of the cylinder. The diameter is given as 3 mm, so the radius \( r \) is half of that: \[ r = \frac{diameter}{2} = \frac{3 \text{ mm}}{2} = 1.5 \text{ mm} \] Next, we can input the radius and height into the volume formula. The height \( h \) is given as 7 mm. Plugging in the values: \[ V = \pi (1.5 \text{ mm})^2 (7 \text{ mm}) \] Calculating \( (1.5 \text{ mm})^2 \): \[ (1.5 \text{ mm})^2 = 2.25 \text{ mm}^2 \] Now, substituting this back into the volume formula: \[ V = \pi (2.25 \text{ mm}^2