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?

(1 point)
Responses

6.2 g/cm3 6.2 g/cm3

0.85 g/cm3 0.85 g/cm3

62 g/cm362 g/cm3

0.62 g/cm3

Answer 1

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

\[
\text{Density} = \frac{\text{mass}}{\text{volume}}
\]

Given that the mass of the roller is 264 grams, we need to find the volume of the cylindrical roller.

The formula for the volume \( V \) of a cylinder is:

\[
V = \pi r^2 h
\]

where \( r \) is the radius and \( h \) is the height.

1. **Calculate the radius**: The diameter is 6 cm, so the radius \( r \) is:
\[
r = \frac{\text{diameter}}{2} = \frac{6 \text{ cm}}{2} = 3 \text{ cm}
\]

2. **Calculate the volume**:
\[
V = \pi (3 \text{ cm})^2 (15 \text{ cm}) = \pi (9 \text{ cm}^2) (15 \text{ cm}) = 135 \pi \text{ cm}^3
\]
Approximating \( \pi \) as 3.14, we get:
\[
V \approx 135 \times 3.14 \approx 423.9 \text{ cm}^3
\]

3. **Calculate the density**:
\[
\text{Density} = \frac{264 \text{ g}}{423.9 \text{ cm}^3} \approx 0.623 \text{ g/cm}^3
\]

Thus, rounding to two decimal places gives us approximately **0.62 g/cm³**.

The correct answer is:

**0.62 g/cm³**