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 per cm cubed

0.85 g/cm3
0.85 g per cm cubed

6.2 g/cm3
6.2 g per cm cubed

0.62 g/cm3

1 answer

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

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

  1. Mass: The mass of the roller is given as 264 grams.

  2. Volume: The volume \( V \) of a cylinder can be calculated using the formula:

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

  • The diameter of the roller is 6 cm, so the radius \( r \) is half of that: \[ r = \frac{6 \text{ cm}}{2} = 3 \text{ cm} \]
  • The height \( h \) of the roller is 15 cm.
  • Now, we can calculate the volume: \[ V = \pi (3 \text{ cm})^2 (15 \text{ cm}) = \pi (9 \text{ cm}^2)(15 \text{ cm}) = 135\pi \text{ cm}^3 \]

Using \( \pi \approx 3.14 \): \[ V \approx 135 \times 3.14 \approx 423.9 \text{ cm}^3 \]

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

Now, rounding to two decimal places gives us approximately \( 0.62 \text{ g/cm}^3 \).

Thus, the correct option is:

0.62 g/cm³