To solve the problem, we need to complete two parts: calculating the volume of the cylinder and calculating its mass.
a) Volume of the Cylinder
The formula for the volume \( V \) of a cylinder is given by:
\[ V = \pi r^2 h \]
where:
- \( r \) is the radius,
- \( h \) is the height.
For the given cylinder:
- \( r = 4 , \text{cm} \)
- \( h = 10 , \text{cm} \)
Now, we plug in the values:
\[ V = \pi (4 , \text{cm})^2 (10 , \text{cm}) \] \[ V = \pi (16 , \text{cm}^2) (10 , \text{cm}) \] \[ V = \pi (160 , \text{cm}^3) \] \[ V \approx 3.14159 \times 160 , \text{cm}^3 \approx 502.654 , \text{cm}^3 \]
Now we round to three significant figures:
\[ V \approx 503 , \text{cm}^3 \]
b) Mass of the Cylinder
The mass \( m \) of the cylinder can be calculated using the formula:
\[ m = \text{density} \times \text{volume} \]
Given:
- Density of wood = \( 0.7 , \text{grams per cm}^3 \)
- Volume \( V \approx 503 , \text{cm}^3 \)
Now, we can calculate the mass:
\[ m = 0.7 , \text{grams per cm}^3 \times 503 , \text{cm}^3 \] \[ m \approx 352.1 , \text{grams} \]
Now rounding to three significant figures:
\[ m \approx 352 , \text{grams} \]
Final Answers
a) Volume of the cylinder: \( 503 , \text{cm}^3 \)
b) Mass of the cylinder: \( 352 , \text{grams} \)