Solving for Area and Circumference of Circles

What number represents π?

• 31.4

• 4.13

• 3.14

• 34.1

Answer explanation

The number that represents π is 3.14, which is the correct answer choice provided.

The distance from the center of a circle to any point on the circle

• radius

• diameter

• circumference

• arc

Answer explanation

The distance from the center of a circle to any point on the circle is called the radius, making it the correct choice among the options provided.

The diameter of the circle measures 7 cm. What is the approximate area of the circle? Use 3.14 for pi.

• 14 cm²

• 22 cm²

• 38 cm²

• 154 cm²

Answer explanation

Remember when calculating the area of a circle with a diameter of 7 centimeters, that you have to actually find the radius first before using the area formula of A = π r².

What is the approximate circumference of the circle? Use 3.14 for pi.

• 14.4 cm

• 22.6 cm

• 45.2 cm

• 162.9 cm

Answer explanation

Find the circumference of the circle with a radius of 7.2 cm using the formula C = 2π r.

What is the approximate area of a circle with a diameter of 15 feet? Use 3.14 for pi.

• 47 square feet

• 177 square feet

• 321 square feet

• 706 square feet

Answer explanation

Before finding the area of a circle with a diameter for 15 feet with the formula A = π r², remember to find the radius of the circle first.

Laura makes a circular tablecloth for her 48 inch diameter table. The tablecloth hangs 6 inches off the edge of the table all the way around. What is the approximate area of the table cloth? Use 3.14 for pi. Hint--draw a diagram of the original table size and then draw the tablecloth around it and label on all sides.

• 1,385 square inches

• 1,810 square inches

• 2,290 square inches

• 2,826 square inches

Answer explanation

This is one for which you really want a picture. Take a look at the diagram. Notice that you will only need the largest circle, but the smaller circle (the table) is needed for finding the diameter of the larger circle (the tablecloth).

It's important to realize that the diameter of the larger circle is 48+6+6=60, making its radius 30 inches. With that, you can find the area using A = π r².

What is the approximate difference in the circumferences of circles K and J? Use 3.14 for pi.

• 150 square feet

• 300 square feet

• 471 square feet

• 942 square feet

Answer explanation

This problem has steps that are easier overall, but there are a lot of places for potential errors. Consider using the formula C = 2 π r since you are given the radii of the circles. Finally, don't miss the fact that this problem asks for the difference between the two circumferences.

The diagram shows a circle inscribed in a square such that the circumference of the circle touches the perimeter of the square at four points. The area of the square is 64 square feet. What is the approximate area of the leftovers if the circle is cut out of the square? Use 3.14 for pi.

• 13.8 square feet

• 25.1 square feet

• 50.3 square feet

• 64.0 square feet

Answer explanation

This is a classic problem when it comes to circle area.

If the square area is 64 feet, you need to find a number that if multiplied by itself, it gives you 64. That number is 8, since (8)(8)=64.

If the length of the square is 8 feet, then that is the diameter of the circle. When finding the area of the circle, be careful to find the radius before using the formula A = π r².

In the end, you have to take the square area and subtract the circle area to get the final answer.

The minute hand on Ms. Scott's clock is 22 inches long, from the center of the clock to its edge. Approximately how far does the minute hand travel around the clock in one hour? (Use 3.14 for pi.)

• 44 inches

• 69 inches

• 138 inches

• 380 inches

Answer explanation

For this problem, you are essentially calculating the circumference (distance around) of a circle with a radius of 22 inches. The tip of the minute hand would travel a circular path once in an hour. Use the formula $C=2\pi r$ .

The circumference of a circle is 25 mm. What is the approximate radius of the circle? Use 3.14 for pi.

• 4 mm

• 5 mm

• 8 mm

• 12 mm

Answer explanation

Write down the formula C = π d. Now, fill in the information you know, that the circumference is 25 and pi is 3.14.

$25\ =\ 3.14d$

Now solve for the diameter.

Be careful, however, as the problem asks you for the RADIUS.