Question

Sofia found a wooden roller in the kitchen. It is in the shape of a cylinder and has a diameter of 6 cm and a height of 15 cm. She weighs the roller and finds that it is 264 grams. Which of the following correctly calculates the density of the roller?

Answer 1

To calculate the density of the roller, we can use the formula:

\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]

Where:
- Mass is given as \(264\) grams.
- Volume can be calculated using the formula for the volume of a cylinder, which is:

\[
\text{Volume} = \pi r^2 h
\]

First, we need to find the radius of the cylinder. The diameter is given as \(6\) cm, so the radius \(r\) is:

\[
r = \frac{\text{Diameter}}{2} = \frac{6 \text{ cm}}{2} = 3 \text{ cm}
\]

Next, we can calculate the volume using the height \(h\) of \(15\) cm:

\[
\text{Volume} = \pi (3 \text{ cm})^2 (15 \text{ cm}) = \pi (9 \text{ cm}^2) (15 \text{ cm}) = 135\pi \text{ cm}^3
\]

Now, we can plug the values into the density formula:

\[
\text{Density} = \frac{264 \text{ g}}{135\pi \text{ cm}^3}
\]

To get a numerical value, we can use an approximation for \(\pi \approx 3.14\):

\[
135\pi \approx 135 \times 3.14 \approx 423.9 \text{ cm}^3
\]

Now, calculating the density:

\[
\text{Density} \approx \frac{264 \text{ g}}{423.9 \text{ cm}^3} \approx 0.623 \text{ g/cm}^3
\]

Thus, the density of the roller is approximately \(0.623 \text{ g/cm}^3\).