Problem Solving with Circles (SUPER)

Beginner Mode

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 $C=2\pi r$ .

Beginner Mode

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.

Beginner Mode

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.

Beginner Mode

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.

Beginner Mode

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.

Intermediate Mode

Andrew runs around a circular track each morning for exercise. The diameter of this track is  $\frac{1}{4}$ mile. Approximately how far will Andrew run if he completes 11 laps around the track?

• 2.2 miles

• 4.3 miles

• 8.6 miles

• 17.3 miles

Answer explanation

The track has a diameter of 0.25 miles. Running a lap around it would be the circumference. Use the formula C = π d to find the circumference.

Do not forget the part that Andrew ran this distance 11 times.

Intermediate Mode

This figure shows two semicircles connected perfectly to a rectangle along their diameters.

What is the approximate area of the figure? Use 3.14 for pi.

• 117.2 ft²

• 136.5 ft²

• 142.0 ft²

• 251.9 ft²

Answer explanation

If the diameter of the semicircles is 7 ft, then the radius is 3.5 ft.

Since there are two semicircles, you can put them together and find the area of a single circle with a radius of 3.5 ft. Use the formula A = π r².

Add the circle area to the rectangle area for the final answer.

Intermediate Mode

This is a drawing of Lane's swimming pool. The pool is rectangular with a semi-circular end.

What is the approximate area of Lane's pool? Use 3.14 for pi.

• 1,000 m²

• 1,628 m²

• 2,256 m²

• 3,512 m²

Answer explanation

First of all, you can split the image into the rectangle and semicircle. That should show you that the 25 m is only the rectangle length, not a part of the semicircle. If the diameter of the semicircle is 40 m, the radius is 20 m.

The formula for the area off a semicircle is $A\ =\ \frac{1}{2}\pi\ r^2$ . Find the area of the semicircle.

Now, add to that area the area of the rectangle.

Intermediate Mode

A circular flower garden has a diameter of 16 ft. A square pond is placed in the center that measures 5 feet on each side. About how much of the garden remains for planting flowers? Use 3.14 for pi.

• 75 ft²

• 176 ft²

• 226 ft²

• 779 ft²

Answer explanation

You essentially need to find two areas and subtract them to solve this problem.

Circle area - square area = answer

Be careful while calculating the circle area, as the formula is A = π r², and they gave you the diameter of 16 ft.

The square has sides of 5 ft, so use those to find the square area.

Intermediate Mode

The diagram below shows the remodeling of Sam's backyard patio. He has removed two congruent semicircle sections for flower gardens. The diameter of each of the semicircle sections is 2 meters.

What is the approximate area of the patio now? Use 3.14 for pi.

• 50 m²

• 54 m²

• 57 m²

• 60 m²

Answer explanation

This problem is essentially a subtraction problem. If you combine the two semi-circles, you can find their area as just one circle with A = π r². Be careful, as you need to use the radius of the circle, not the given diameter of 2 m.

Rectangle area - circle area = answer