Diameter of a circle

### 1.1. Knowledge to remember

Take cardboard, draw and cut a circle with a radius of 2cm. We mark a point A on the circle.

Place point A on the 0 line on a ruler with centimeter and millimeter divisions. We let the circle roll once on that ruler, then we see that point A rolls to the position of point B which is between 12.5cm and 12.6cm on the ruler. The length of a circle with radius 2cm is the length of line segment AB.

The length of a circle is called its circumference.

Thus, a circle with a radius of 2cm has a circumference between 12.5cm and 12.6cm or a circle with a diameter of 4cm has a circumference between 12.5cm and 12.6cm.

In math, one can calculate the circumference of a circle with a diameter of 4cm by multiplying the diameter of 4cm by the number 3.14:

4 x 3.14 = 12.56 (cm)

To calculate the circumference of a circle, multiply the diameter by 3.14.

**C = dx 3.14**

(C is the circumference of the circle, d is the diameter of the circle).

Or: To calculate the circumference of a circle, we multiply the radius by 2 times the number 3.14.

**C = rx 2 x 3.14**

(C is the circumference of the circle, r is the radius of the circle).

**Example 1:** Find the circumference of a circle with radius 6cm.

The circumference of a circle is:

6 x 3.14 = 18.84 (cm)

**Example 2:** Find the circumference of a circle with radius 5cm.

The circumference of the circle is:

5 x 2 x 3.14 = 31.4 (cm)

### 1.2. Solving textbook exercises on page 98

**Lesson 1 of the textbook page 98:**

Find the circumference of a circle with diameter d:

a) d = 0.6cm; b) d = 2.5dm; c) \(\frac{4}{5}\) m.

__Solution guide:__

a) Perimeter of the circle is:

0.6 × 3.14 = 1.884(cm)

b) The circumference of the circle is:

2.5 × 3.14 = 7.85(dm)

c) Change: \(\frac{4}{5}\)m = 0.8m

The circumference of the circle is:

0.8 × 3.14 = 2.512(m)

Lesson 2 Textbook page 98:

Find the circumference of a circle with radius r:

a) r = 2.75cm; b) r = 6.5dm; c) r = \(\frac{1}{2}\)m

__Solution guide:__

a) Perimeter of the circle is:

2.75 × 2 × 3.14 = 17.27 (cm)

b) The circumference of the circle is:

6.5 × 2 × 3.14 = 40.82(dm)

c) The circumference of the circle is:

\(\frac{1}{2}\) × 2 × 3.14 = 3.14(m)

Lesson 3 Textbook page 98:

A car wheel has a diameter of 0.75m. Calculate the circumference of that wheel.

__Solution guide:__

The circumference of the wheel is:

0.75 x 3.14 = 2,355 (m)

Answer: 2,355m.

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