Question

A solid cylinder has a radius of 4 cm and a height of 10 cm.
<<-4 cm -
10 cm
a) Work out the volume of the cylinder.
Give your answer correct to 3 significant figures.
The cylinder is made of wood.
The density of the wood is 0.7 grams per cm³
b)
Work out the mass of the cylinder.
Give your answer correct to 3 significant figures.

Answer 1

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: \( 352 \, \text{grams} \)