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Chapter 3: Problem 79

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

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

Step by step solution

01

- 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.
02

- 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.
03

- Plug in the given values into the formula

Using \(r = 3 \mathrm{cm}\) and \(h = 6 \mathrm{cm}\), the volume formula becomes: \[ V = 3.14 \times (3)^{2} \times 6 \]
04

- Calculate the volume

First, calculate \( (3)^{2} \): \[ (3)^{2} = 9 \] Then, multiply \( 9 \times 6 \): \[ 9 \times 6 = 54 \] Finally, multiply by \(3.14\): \[ 54 \times 3.14 \approx 169.56 \mathrm{cm}^{3} \]
05

- Round to the nearest full cm

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

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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 (\

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