Question

What is the volume of a cylinder with a radius of \(3 \mathrm{~cm}\) and a height of \(6 \mathrm{~cm}\) (take \(\pi\) as \(3.14\) and work to the nearest full \(\mathrm{cm})\) ?

Short answer

The volume of the cylinder is \(170 \mathrm{cm}^{3}\).

Step-by-step solution

- Identify the given values

The cylinder's radius is given as 3 cm and the height is given as 6 cm. These values are essential for calculating the volume.

- Recall the formula for the volume of a cylinder

The formula for the volume of a cylinder is \[ V = \pi r^{2} h \] where: \(V\) is the volume, \(r\) is the radius, and \(h\) is the height.

- Plug in the given values into the formula

Using \(r = 3 \mathrm{cm}\) and \(h = 6 \mathrm{cm}\), the volume formula becomes: \[ V = 3.14 \times (3)^{2} \times 6 \]

- Calculate the volume

First, calculate \( (3)^{2} \): \[ (3)^{2} = 9 \] Then, multiply \( 9 \times 6 \): \[ 9 \times 6 = 54 \] Finally, multiply by \(3.14\): \[ 54 \times 3.14 \approx 169.56 \mathrm{cm}^{3} \]

- Round to the nearest full cm

The volume rounded to the nearest full cm is \(170 \mathrm{cm}^{3}\).

Key concepts

geometry formulas

In geometry, formulas are essential tools that help us calculate different attributes of shapes. When dealing with three-dimensional shapes like cylinders, formulas can be used to determine properties such as volume and surface area.

The formula for the volume of a cylinder is straightforward: \( V = \pi r^{2} h \). This tells us that the volume (\