1. Module 3

1.14. Page 4

Mathematics 10-3 Module 3 Lesson 3

Module 3: Linear Measure

 

Bringing Ideas Together

 

three-dimensional object: an object having length, width, and height or depth

 

An object in which one of its three dimensions is not relevant may be considered to be a two-dimensional object. For example, a thin sheet of paper may be considered to be a 2-D object, but a rectangular wooden block would normally be considered 3-D.

In the Get Started and Explore sections, you investigated finding the centre of a three-dimensional object, such as a rectangular board or a circular disk.

 

The next few examples apply the new skills you have acquired.

 

Example 3

 

John wants to drill a hole at the centre of a circular disk. He used his carpenter’s square to locate the centre. He wants to check the radius before he drills. If the disk has a diameter of what is the radius of the circular disc?

 

Solution

 

First, estimate your answer. The radius is half the length of the diameter. The radius of the disc should be a little more than 4 in, since the diameter is a little longer than 8 in and

 

Method 1

 

Divide fractions.

 

 

 

The radius is This answer is reasonable, as the estimate was a little more than 4 in.

 

Method 2

 

Use decimals and your calculator.

 

 

 

So,

 

 

 

Therefore,

 

 

 

The radius is 4.1875 in.

 

Note:

 

So,

 

 

 

The radius if the disk is

 

Example 4

 

A 2 × 4 board is long. Where should this board be marked in order to cut the board into two shorter 2 × 4 boards of equal lengths? Express your answer as a whole number and fraction.

 

Solution

 

Method 1

 

Divide fractions.

 

 

 

Method 2

 

Divide the whole number separately from the fractional part.

 

 

 

Method 3

 

Use decimals.

 

 

 

So,

 

 

 

The stud should be marked in from one end to cut it into two equal lengths.

 

Self-Check

 

It is time to apply your problem-solving skills to locate midpoints. When you are finished, check your answers.

 

SC 5. Masie wants to drill halfway through a 2 × 4 piece of lumber, which is thick. How deep should she drill?

 

SC 6. Marty wishes to locate the centre of a circular disk with a diameter of What is the radius of the disk?

 

SC 7. Randy wants to drill a hole in the centre of a drawer front. If the front of the drawer is 30 cm × 15 cm, where is the centre located from the edges of the drawer front?

 

SC 8. Where should a board long be cut to obtain two equal lengths?

 

Compare your answers.

 

Mastering Concepts

 

Try this question. When you are finished, check your answer.

 

Suppose you were given a triangular piece of wood with three equal sides. How would you locate the centre of the wood?

 

Compare your answer.