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Guided Practice

You can also use the radius of a circle to estimate and calculate the circumference of the circle. The radius is half the length of the diameter. So, if the circumference is π × diameter, then circumference is also π × (2 × radius).

The circumference of this circle is 2 × 1.6 × π kilometers.

The diameter of a circle is the distance across the circle through its center.

The perimeter, or circumference, of a circle is equal to π × the .

The circumference of a circle is equal to approximately × the diameter.

Use the diameter of the circle to calculate its circumference exactly.

Circumference = × π centimeters

Use the diameter of the circle to calculate its circumference exactly.

Circumference = × π inches

Use the diameter of the circle to calculate its circumference exactly.

Circumference = × π feet

Approximate the circumference of the circle.
Use π ≈ 3.14.

Circumference ≈ yd

Approximate the circumference of the circle.
Use π ≈ 3.14.

Circumference ≈ km

Approximate the circumference of the circle.
Use π ≈ 3.14.

Circumference ≈ inches

Approximate the circumference of the circle.
Use π ≈ 3.14.

Circumference ≈ centimeters

Approximate the circumference of the circle.
Use π ≈ 3.14.

Circumference ≈ feet

Determine the exact circumference of a circle which has a radius of 4.5 yards.

Circumference = × π yards

Study the image. The area of the largest circle is made up of all the different circumferences shown (plus infinitely many more that aren't shown). All these circumferences can be unwrapped to form a triangle, so the area of the circle is equal to the area of the triangle. The height of the triangle is the radius of the circle, r.

Let the largest green circumference be 2πr. Then the area of the triangle is 1/2(2πr)(r). This is equal to πr2. So the area of the circle is πr2.

The example shows that the area of a circle can be given by the formula A = π × radius2.

What is the area of a circle with a radius of 1 unit?

Area = × π square units

What is the area of a circle with a radius of 2 inches?

Area = × π square inches

Approximate the area of a circle with a radius of 2 inches. Use π ≈ 3.14.

Area = square inches

Approximate the area of a circle with a diameter of 8 inches. Use π ≈ 3.14.

Area = square inches

What is the area of a circle with a radius of 7 centimeters?

Area = × π square centimeters

Approximate the area of a circle with a radius of 6 centimeters. Use π ≈ 3.14.

Area = square centimeters

Approximate the area of a circle with a radius of 5.5 inches. Use π ≈ 3.14.

Area = square inches

A playground is built in the shape of a circle. How much fencing is needed to enclose the playground?

First decide whether you need to determine circumference or area. We need the length of fencing around the circle, so we want the circumference. Next, use a formula for circumference to calculate:

C  = π × diameter

C ≈ 3.14 × 64 m

You will need approximately 200.96 meters of fencing.

Enter circumference or area and then solve the problem. Use 3.14 for π.

A Ferris wheel has a diameter of 250 feet. How many feet does the Ferris wheel rotate in one full turn?

You need to determine the .

The wheel turns ft in one full turn.

Enter circumference or area and then solve the problem. Use 3.14 for π.

How much material is needed to cover the top of the circular drum shown?

You need to determine the .

You need square inches of material.

Enter circumference or area and then solve the problem. Use 3.14 for π.

A manhole cover has a radius of 30 cm. How much space does the top of the manhole cover take up?

You need to determine the .

The cover takes up square cm.

A circle has a circumference of 36.31 meters. What is the approximate radius of the circle? Use 3.14 for π and round to the nearest hundredth.

The approximate radius is meters.

Tim takes 5 minutes to jog around a circular track with a diameter of 400 meters. How fast is Tim jogging? Use 3.14 for π.

Tim is jogging meters per minute.

C: pixels

A:   square pixels

     

add circle

clear

When you flip a penny, the coin can land on heads or tails. The probability that it lands on heads is 1/2.

What if both sides of the penny were tails? Then the probability of landing on heads would be 0, which means it's impossible. If both sides of the penny were heads, then it would be certain to land on heads, and the probability of heads would be 1.

Complete the statement with the best estimate of the probability: either 0, 1/2, or 1.

The probability of flipping a coin and landing on both heads and tails is .

Complete the statement with the best estimate of the probability: either 0, 1/2, or 1.

The probability of choosing a white sock from a drawer of all white socks is .

Complete the statement with the best estimate of the probability: either 0, 1/2, or 1.

The probability of rolling a 6 on a dice when you have already rolled a 4 is .

Complete the statement with the best estimate of the probability: either 0, 1/2, or 1.

The probability of choosing a white sock from a drawer with one black sock and one white sock is .

Complete the statement with the best estimate of the probability: either 0, 1/2, or 1.

The probability of choosing a white sock from a drawer with 4 white socks and 4 black socks is .