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 62 g/cm3 62 g/cm3 6.2 g/cm3 6.2 g/cm3 0.62 g/cm3 0.62 g/cm3 0.85 g/cm3 0.85 g/cm3

Answer 1

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

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

1. **Given Data**:
- Mass of the roller = 264 grams
- Diameter of the roller = 6 cm → Radius = Diameter/2 = 3 cm
- Height of the roller = 15 cm

2. **Calculate the Volume of the Cylinder**:
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.

Substituting the values:

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

Approximating \(\pi\) as \(3.14\):

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

3. **Calculate Density**:
Now we can find the density:

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

Rounding this value gives us approximately \(0.62 \, \text{g/cm}^3\).

4. **Conclusion**:
Among the choices provided, the correct answer is:

**0.62 g/cm³**