Circumference of a Circle Objective: Investigate & explain the relationships among radius, diameter, and circumference.

Distance around a circle: The distance around a circle is its circumference. For any circle, the circumference C, divided by the diameter, d, is approximately 3.

The circumference of a circle is also the perimeter of the circle! Circumference divided by diameter equals 3. or C/d = 3

The ratio C/d = π Pi is a decimal that never repeats and never terminates. π cannot be written as a fraction, For this reason, we call π an irrational number.

C = πd Since the diameter is twice the radius, the circumference is also π multiplied by 2r. We write: C = π x 2r, or C = 2πr

When we know the radius or diameter of a circle, we can use one of the formulas to find the circumference of a circle.

The face of a toonie has a radius of 1.4 cm To find the diameter of the face: The diameter = 2r, where r is the radius. Substitute: r = 1.4; d = 2x1.4 =2.8 The diameter is 2.8 cm.

Circumference is a length, so its units are units of length such as centimetres, metres, or millimetres.

To find the circumference of the face: C = πd Substitute d = 2.8 C = π x 2.8 = = 8.8 cm to one decimal place

or… C = 2πr Substitute: r = 1.4 C = 2 x π x 1.4 = = 8.8 cm to one decimal place.

We can estimate to see if the answer is reasonable: The circumference is approx. 3 times the diameter. 3 x 2.8 cm = 3 x 3 cm = 9 cm The circumference is approximately 9 cm. The calculated answer is 8.8 cm, so this answer is reasonable.

When we know the circumference, we can use a formula to find the diameter.

C = πd To isolate d (get d by itself), divide each side by π C/π = πd/π C/π = d So, d = C/π

An above-ground circular swimming pool has a circumference of 12 m. Calculate the diameter and radius of the pool. Give answers to the two decimal places. Check if the answers are reasonable.

Solution The diameter is: d = C/π Substitute: C = 12 d = 12/π - use a calculator; do not clear your calculator = The radius is 1/2 the diameter, or r = d/2 Divide the number in the calculator display by 2.

Solution continued… r = The diameter is 3.82 m to two decimal places. The radius is 1.91 to two decimal places.

Since the circumference is approx. 3 times the diameter, the diameter is about 1/3 the circumference. One=third of 12 m is 4 m. So the diameter is about 4 m. The radius is 1/2 the diameter. 1/2 of 4 m is 2 m. The radius of the pool is about 2 m. Since the calculated answers are close to the estimates, the answers are reasonable.

Practice, pages #s 1a, 2a, 3-8. This is due and will be corrected/handed in on Wednesday, March 12:)

The 2 circles are congruent Remember that congruent shapes are identical. They are shapes that match exactly. A circle with a radius of 5 cm has a diameter of 10 cm. What is the diameter of a circle that has a radius of 3 cm? What is the radius of a circle that has a diameter of 24 cm?

How to use a protractor to measure angles. Video

Assignment Because of skiing tomorrow, this assignment is due on Monday, March 10, We will correct at the beginning of class. Pages , #s 1-6