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.

1 answer

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