ISEE Upper Level Math : How to find circumference

Example Questions

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Example Question #1 : Know And Use The Formulas For The Area And Circumference Of A Circle: Ccss.Math.Content.7.G.B.4

What is the circumference of a circle with a radius equal to ?

Explanation:

The circumference can be solved using the following equation:

Example Question #1 : How To Find Circumference

The radius of a circle is . Give the circumference of the circle in terms of .

Explanation:

The circumference can be calculated as , where is the radius of the circle.

Example Question #2 : How To Find Circumference

The area of a circle is . Give the circumference  of the circle in terms of .

Let .

Explanation:

The area of a circle can be calculated as , where   is the radius of the circle.

The circumference can be calculated as , where is the radius of the circle.

Example Question #3 : How To Find Circumference

What is the circumference of a circle with a radius of ?

Explanation:

The circumference can be solved using the following equation:

Where  represents the radius. Therefore, when we substitute our radius in we get:

Example Question #5 : Know And Use The Formulas For The Area And Circumference Of A Circle: Ccss.Math.Content.7.G.B.4

The perimeter of a given rectangle is equal to the circumference of a given circle. The circle has radius  inches; the width of the rectangle is  inches. What is the length of the rectangle?

inches

inches

inches

inches

inches

inches

Explanation:

The circumference of a circle with radius  inches is

inches.

The perimeter of the rectangle is therefore  inches. To find its length, substitute  and  into the equation and solve for :

inches

Example Question #4 : How To Find Circumference

The area of the shaded region in the above diagram is . Give the circumference of the circle.

Explanation:

The shaded region is an  sector; this represents

of the circle. The area of the region is therefore

,

where  is the radius. Setting  and solving for :

The circumference of a circle is its radius multiplied by , or

Example Question #4 : How To Find Circumference

A circle has a radius of 5 miles, what is its circumference?

Explanation:

A circle has a radius of 5 miles, what is its circumference?

To find circumference, use the following formula:

Plug in 5 miles to get our answer:

Example Question #5 : How To Find Circumference

While mailing some very important letters, you decide to use your circular rubber stamp. If the stamp has a radius of 3.5 cm, what is the circumference of the stamping surface?

Cannot be determined from the information provided.

Explanation:

While mailing some very important letters, you decide to use your circular rubber stamp. If the stamp has a radius of 3.5 cm, what is the circumference of the stamping surface?

Find circumference via the following:

Where r is our radius, which is 3.5 cm.

Example Question #6 : How To Find Circumference

You have a circular window in your vacation room. It has a radius of 9 inches. What is the circumference of the window?

Explanation:

You have a circular window in your vacation room. It has a radius of 9 inches. What is the circumference of the window?

Begin with the formula for circumference of a circle.

Next, plug in our "r" and solve for C

Example Question #7 : How To Find Circumference

Find the circumference of a circle with a radius of 4cm.

Explanation:

To find the circumference of a circle, we will use the following formula:

where r is the radius of the circle.

Now, we know the radius of the circle is 4cm.

Knowing this, we can substitute into the formula.  We get

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