Test 2: Circles and Composite Figures

Test 2:

Circles and Composite Figures Study Guide

In your notebook, be sure to take notes. Remember that you can use them on your test. Be sure to write down any strategies, formulas, or vocabulary words that can help you. (If you don't have your notebook, use another sheet of paper.)

​Things To Know For This Test

​1. Unit Rates

​2. Parts of A Circle

​3. Area and Circumference of a Circle

​4. Area of Composite Figures

​5. Area of the Shaded Region

Unit Rates​

Remember unit rates are a ratio of one measurement to another when one of the measurements is one.

​

​Example: When Angel is running, he can run 12 miles in 2 hours. A unit rate for this ration would be: Angel runs 6 miles in one hour.

​Calculating Unit Rates

​To calculate a unit rate, divide both measurements by the measurement that you want to become one.

Example:

​In the picture, the rate of loaves to hours is 40 loaves every 8 hours. Since we want to know loaves for one hour, we'll divide by the number of hours.

​40 divided by 8 is 5 and 8 divided by 8 is 1.

Multiple Choice

You spend $40 on 5 pounds of concrete. What is the unit rate in dollars per pound?

• $8 per pound
• $5 per pound
• $35 per pound
• 0.125 pounds per dollar

Multiple Choice

6 movie tickets cost $30.00. What is the cost per ticket (unit rate)?

What will you do to find the unit rate?

• multiply by 6 to get $180 per ticket

• divide by 6 to get $5 per ticket

• multiply by 30 to get $900 per ticket

• divide by 30 to get $1 per ticket

Parts of A Circle​

​You should be able to identify the diameter, radius, circumference, and area of a circle.

​Parts of A Circle

• ​The circumference is the distance around the circle. (Perimeter, edge)

• ​The diameter is the LONG line that cuts a circle in half. It must pass through the center.

• ​The radius is the SHORT line that goes from the edge of the circle to the center.

• ​The area is the amount of space inside the circle.

Radius and Diameter

• The diameter is two times the length of the radius.

  • ​If the diameter is 10 inches, the radius is 5 inches.

• ​The radius is half of the length of the diameter.

  • ​If the radius is 4cm, the diameter is 8cm.

Multiple Choice

The distance halfway across the circle is called the...

• radius
• diameter
• circumference
• area

Multiple Choice

If my radius is 10ft, what is my diameter?

• 20ft
• 5ft
• 31.4ft
• 62.8ft

Multiple Choice

A circle has a diameter of 36 ft. What is the radius?

• 18

• 72

• 14

Multiple Choice

Is the red line a radius or diameter of the circle?

• Radius
• Diameter

Multiple Choice

Is the red line a radius or diameter of the circle?

• Radius
• Diameter

Multiple Choice

What does "circumference" mean?

• Space a circle takes up
• Distance around a circle
• Line from one side of a circle to another
• Line from center of circle to side

Multiple Choice

What is the formula for circumference of a circle given the diameter?

• C = pi x r
• C = pi x 2r
• C = pi x D
• C = pi x 2D

Multiple Choice

What is the formula for circumference of a circle given the radius?

• C = pi x r
• C = pi x 2r
• C = pi x D
• C = pi x 2D

Multiple Choice

Steven purchases a bowl. The diameter of the bowl is 14 cm. What is the circumference of the bowl?

• 28 cm
• 43.98 cm
• 87.96 cm
• 7 cm

Multiple Choice

Daniel wants to buy cookies for her friend. The radius of a cookie is 5 inches. What is the cookie’s circumference?

• 10 in
• 2.5 in
• 15.7 in
• 31.4 in 

Multiple Choice

What is the circumference of this circle?

• 3.14 cm 
• 37.7 cm
• 24 cm
• 68.4 cm

Multiple Choice

What is the formula for finding the area of a circle?

• A = π·d

• C = 2·π·r

• A = π·r²

• C = π·d

Multiple Choice

What does r represent in the formula:

A = π·r²

• circumference

• radius

• diameter

• squared

Multiple Choice

What number does π represent?

• 4.13

• 3.41

• pie

• 3.14

Multiple Choice

Find the area of the circle.

• 18.84 m²

• 113.04 m²

• 37.68 m²

• 452.16 m²

Multiple Choice

Find the area of the circle.

• 12.56 cm²

• 25.12 cm²

• 50.24 cm²

• 200.96 cm²

Multiple Choice

Find the area of the circle

• 56.52
• 254.34
• 1017.36
• 113.04

Working Backwards

​Sometimes, you might be given the circumference of a circle and asked to calculate to diameter, radius or area.

​To work backwards, divide the circumference by pi to find the diameter.

​Once you have the diameter, you can divide it by two to calculate the radius.

​Finally, once you have the radius you can use the area formula to calculate the area.

Multiple Choice

A ball has a circumference of 9.42 cm. What is the diameter?

• 29.5788 cm
• 59.1576 cm
• 3 cm
• 1.5 cm

Multiple Choice

• A

• B

• C

• D

Pi

​Pi is the ratio of the circumference to the diameter. Pi is equal to the circumference divide by the diameter.

​

​Pi is also equal to 3.14

Multiple Choice

Which of these best describes $$\pi?$$  

• The square root of the area of a circle.

• The ratio of the radius of a circle to its diameter.

• The radius of a circle times 3.14. 

• The ratio of the circumference of a circle to its diameter.

Multiple Choice

Which of the following equations represents the relationship between the circumference, C, and the diameter, d, of any circle?

• $$C\ =\ \pi r$$

• $$Cd\ =\pi$$

• $$\pi=\ \frac{C}{r}$$

• $$\pi=\frac{C}{d}$$

Multiple Choice

What number is pi?

• 1.41

• 3.14

• 2

• 5.14

​Area of Composite Figures

​Composite figures are figures made up of more than one shape.

​

​The figure to the right is made up of a rectangle and a square on top. To find the area of the figure, we would find the area of the square and then find the area of the rectangle and add them together.

Multiple Choice

Calculate the area. Use 3.14 for pi. Round to the nearest tenth if needed.

• 50.2 m ²

• 23.1 m ²

• 14.7 m ²

• 25.6 m ²

Multiple Choice

You can use the STAAR Resource sheet to find your formulas?

• True
• False

​Area of the Shaded Region Problems

​When you are given a figure and asked to find the area of only the shaded region, you should find the area of each shape. Then, subtract the area of the smaller shapes from the area of the larger shape that is shaded.

Multiple Choice

Both circles have the same center. Find the area of the shaded region. Use 3.14 for π and round your answer to the nearest hundreth.

• 122.46 mi²

• 122.45 mi²

• 175.84 mi²

• 175.85 mi²

Multiple Choice

What is the approximate area of the shaded region? (Round to the nearest whole number)

• 58

• 80

• 30

• 100