What is the mass of a cylinder of lead with a radius of 1 centimeter and a height of 3 centimeters, given that the density of lead is 11.4 g/cm^3

Answer 1

To calculate the mass of a cylinder, we first need to find its volume and then use the density to find the mass. Here are the steps:

1. **Find the volume of the cylinder**:
The volume \(V\) of a cylinder is given by the formula:
\[
V = \pi r^2 h
\]
where \(r\) is the radius and \(h\) is the height.

Given:
- Radius \(r = 1\) cm
- Height \(h = 3\) cm

Plugging in the values:
\[
V = \pi (1^2) (3) = 3\pi \text{ cubic centimeters}
\]
Since \(\pi \approx 3.14159\):
\[
V \approx 3 \times 3.14159 \approx 9.42477 \text{ cubic centimeters}
\]

2. **Calculate the mass of the cylinder**:
The mass \(m\) can be found using the density formula:
\[
m = \text{density} \times \text{volume}
\]

Given the density of lead \(\rho = 11.4 \text{ g/cm}^3\):
\[
m = 11.4 \times 9.42477 \approx 107.442 \text{ grams}
\]

So, the mass of the lead cylinder is approximately \(107.442\) grams.