Measurement, Perimeter, and Area for CBEST Exam Study Guide (page 3)
There are certain numbers, formulas, and measurements, such as decimal equivalents, area formulas, and weight conversions, that you will be expected to know when working some CBEST problems. It's a good idea to put them on flash cards for memorization.
You will be asked to figure problems using measurements of length, weight, and volume as well as speed, time, and temperature. Here are the common measurements you may be asked to use. Knowledge of the metric system was not on the CBEST when this book went to print.
Weight measurements are usually measured on a scale.
- 1 pound = 16 ounces
- 1 ton = 2,000 pounds
Liquid and Dry Measurements
Liquid and dry measurements are usually made in a measuring spoon, cup, or larger container. Think of the dairy department of your grocery store. Units smaller than a cup probably will not be on the test.
- 1 cup = 8 ounces
- 1 pint = 2 cups = 16 ounces
- 1 quart = 2 pints
- 1 quart = 4 cups = 32 ounces
- gallon = 2 quarts
- gallon = 4 pints = 8 cups
- gallon = 64 ounces
- 1 gallon = 2 half gallons
- 1 gallon = 16 cups = 4 quarts
- 1 gallon = 128 ounces
Distance can be measured by rulers or tape measures. In a car, miles are measured by an odometer.
- 1 foot = 12 inches
- 1 yard = 3 feet
- 1 yard = 36 inches
- 1 mile = 5,280 feet
- 1 mile = 1,760 yards
Square and Cubic Measurements
Here are some conversions you should know. You won't need to memorize any of the larger numbers on the CBEST—just be able to figure them out if you need them.
- 1 square foot = 144 square inches
- 1 cubic foot = 12 × 12 × 12 inches or 1,728 cubic inches
- 1 yard = 3 feet
- 1 square yard = 9 square feet
- 1 cubic yard = 27 cubic feet
Temperature is measured by a thermometer in degrees. The only tricky thing here is to be clear on the distinction between "above zero" and "below zero" numbers. If you can't visualize the distance between 40 below and 65 above 0, a rereading of Math Lesson 2 on negative numbers might help.
Speed is usually measured by speedometers in miles per hour. Time, distance, and rate problems are discussed in Math Lesson 7.
Time can be measured by a clock or by a calendar. You can figure out the number of seconds in an hour (3,600) by multiplying 60 seconds by 60 minutes.
- 1 minute = 60 seconds
- 1 hour = 60 minutes = 3,600 seconds
- 1 day = 24 hours = 1,440 minutes
- 1 week = 7 days = 168 hours
- 1 year = 12 months = 52 weeks = 365 days
Sample Measurement Question
- Samuel, a friend of yours, has an uncle in the wholesale fertilizer business. "And I don't even have a garden," he remarks to you one day. The two of you decide to make a garden in a 21 ft. by 25 ft. patch in his back yard. You suggest he put 4 inches of his uncle's fertilizer on the top and then dig it in. He asks you to help him decide how much to order. Try to solve your friend's problem in cubic feet and write down your answer.
- 9,600 cubic yards
- 58.3 cubic yards
- 19.4 cubic yards
- 6.5 cubic yards
- none of these
You give Samuel your answer and he calls his uncle. His uncle is most obliging, but insists that since he's a wholesale dealer, he can only accommodate orders in cubic yards. He also warns Samuel that his fertilizer does not smell very good, and needs to be dug in right away. You re-figure your calculation in terms up cubic yards. You finally come up with a figure and Samuel calls his uncle. What is the amount he orders?
Look for your answer below and read to discover the exciting conclusion.
- 9,600 cubic yards. Suddenly, it grows dark. You try looking out the window, but fertilizer is stacked up against the window as high as you can see. You can't even get out of your house. You changed everything to inches and divided by 36 because there are 36 inches in a yard, so how could you have been wrong?
- 58.3 cubic yards. Suddenly, it grows dark. Your windows are covered with fertilizer. Fertilizer is piled to the roof and the garden is buried. You changed inches to feet and divided by 3, so where did you go wrong?
- 19.4 cubic yards. There is a pile of fertilizer about three feet high covering your garden. This is more than you expected so you pile it up and give it to your neighbors. You were clued into the cube idea and divided by 9, so why didn't you get it right?
- 6.5 cubic yards. You spread exactly 4 inches on top of the garden with a rake. Quickly, you and Samuel dig the fertilizer under. You feel proud that you could get the right answer to a complicated math problem.
- You couldn't find your answer, so redo your math. Choose the closest answer.
In this volume problem, three dimensions need to be multiplied to get a cubic measurement, but they need to be in the same units of measurement. You can't multiply 21 feet by 4 inches. In this case, it is easiest to change the 4 inches into feet. Four inches is of a foot and of 21 is 7. Seven times 25 is 175, the answer to the first part of the question. Now that you're working in cubic feet, you need to convert to cubic yards.
Suppose you had a square with sides of one yard each. Since there are 3 feet in a yard, a square yard would include 9 square feet.
Now suppose you made your square into a cube. You would have 3 layers of 9, or 27 cubic feet. So since you need 175 cubic feet of fertilizer, you should divide by 27 cubic feet: 175 ÷ 27 ≈ 6.5 cubic yards.
Try your hand at some additional measurement problems.
- Casey bought 3 lbs. 5 oz. of boneless chicken at $1.60 per pound. How much did she pay?
- Frank cut 2'8" off a 6'3" board. How much was left?
- cannot be determined
- Eight scouts each need two 3' dowels for some banners they are making. Before being cut, the dowels are 10 feet long. How many dowels should the scoutmaster buy?
- Three full containers each held one of the following amounts: one ounce, one cup, and one quart. If all three containers were dumped into a gallon jar, how much room would be left?
- A strip of wallpaper was 5 yards long and 5 inches wide. How many square feet of wallpaper were there?
- Cooking a turkey takes 20 minutes for every pound in an oven heated to 350°. If a turkey weighing 20 pounds has to be ready by 2:00 P.M. at the latest, when should the turkey be put in the preheated oven?
- 6:20 a.m.
- 6:40 a.m.
- 7:00 a.m.
- 7:20 a.m.
- 7:40 a.m.
On the CBEST, there is usually one question that goes something like this:
A school of 240 children want to go on a field trip. A bus can hold 50 children. How many buses are needed? Among the answers are 4, , and 5. Four buses would not be enough. There is no such thing as of a bus. So 5 is the answer.
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