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Exercise 18. Review Problems
1. A piece of ribbon 11 yards long was cut into 9 equal pieces for badges for ushers at a school entertainment. How many inches long was each badge?
2. If a recipe called for 1 cup of sugar and a measuring cup was not at hand, how many level tablespoons of sugar should be used? (1 cup =16 tablespoons.)
3. A pint of vinegar weighs approximately how much?
4. If you did not have a scales and a recipe called for 1 pound of sugar, how many cups of sugar should you use?
5. A box of apples usually weighs about 40 pounds, net. How much does a grocer get per box if he retails them at 12 cents a pound? (40 lb. net means without the weight of the box.)
6. One sized can of Karo syrup is labeled 23 pounds net. Express the approximate size of the can in liquid measures.
7. A farmer sold a load of wheat. The weight of the loaded wagon was 3045 pounds. The wagon and empty sacks weighed 1125 pounds. How many bushels of wheat were there in the load?
8. What is the only state in which 56 pounds of shelled corn is not considered a bushel? (See page 216.) How many pounds make a bushel in that state?
9. How many pounds of the following products make a bushel in your state: apples, rye, oats, beans, onions, potatoes, buckwheat, peas?
10. How many minutes are there in a year? How many seconds?
11. Captain Alcock flew across the Atlantic Ocean in an aeroplane in 16 hours and 12 minutes. Approximately what part of a day did it take for the flight? How many minutes did it take him?
12. If a manual training teacher pays 70 cents for a box (containing a gross) of screws, how much must he charge the pupils for each screw to sell them approximately at cost?
13. A family uses 2 quarts of milk per day. At that rate, approximately how many barrels will they use in a year?
14. How many bushels of wheat will a bin hold that is 12 feet long, 6 feet wide and 5 feet deep?
Short Method: Since 4 bushels of grain occupy 5 cubic feet of space, there are as many bushels as there are cubic feet of space. We find the number of cubic feet by multiplying the length by the width by the depth. We may then find the number of bushels by multiplying the product of the length, width and depth by g. Use cancellation for shortening the work:
12x6x5x4=288, the no. of bu.
15. How many bushels of oats will a bin hold that is 10 feet long, 8 feet wide and 6 feet deep?
10X8X6X = ?
16. A bin 16 feet long, 10 feet wide and 62 feet deep is full of rye. How many bushels of rye are there in the bin?
17. How many bushels of wheat can be put into a bin 8 feet long, 47 feet wide and 6 feet deep?
18. A bin is 16 feet long, 8 feet wide and 7 feet deep. How many bushels of shelled corn will this bin hold?
19. How many bushels of oats can be placed in a bin 12 feet long, 10 feet wide and 54 feet deep?
An angle is a figure formed by two lines meeting at a point.
Take a sheet of paper and fold one portion
of an edge over on the other portion. Then crease across the paper and open the sheet of paper. The crease will form two angles with the edge of the paper. How
do these angles compare in size? When one line meets another line so that the two angles formed are equal, the angles are
called right angles. An angle that is smaller than a right angle is called an acute angle. The angle at the top of the page is an acute angle. Draw an acute angle on the blackboard.
An angle that is larger than a right angle is called an obtuse angle. The angle at the left is called an obtuse angle. Draw an obtuse angle on the
blackboard. These different kinds of angles will be useful in describing rectangles, parallelograms, triangles and many other figures.
Exercise 1. Rectangles
1. How many straight lines form the rectangle shown at the left?
2. How many angles has a rectangle?
3. What kind of angles are these four angles? A rectangle is a figure bounded by four straight lines and haring four right angles.
4. Name various things in the room which are rectangular in shape. For example: the blackboard, the window panes.
6. What kind of units of measure do we use in describing the area or size of a rectangle?
Area of a Rectangle
6. What is the area of a rectangle 4 feet long and 3 feet wide?
7. How many square feet are there in
one row a foot wide along the base? 8. How many such rows are there in the rectangle? Then how many square feet are there in the area of the rectangle?
In the same way show how to find the area of a rectangle: 9. 12 in. long and 8 in. wide. 11. 8 yd. long and 5 yd. wide. 10. 15 ft. long and 12 ft. wide. 12. 40 rods long and 20 rods wide.
13. In each of these rectangles how does the number of squares in one row compare with the number units of length in the base?
14. How does the number of rows of squares compare with the number of units of length in the width?
We have already seen that the area of a rectangle is found by multiplying the number of squares in one row by the number of rows. This is often expressed in the shorter form:
The area of a rectangle is equal to the product of its base and altitude.1 The line representing the length of the rectangle is usually called the base and the line representing the width is called the altitude.
1. The length of a blackboard is 12 feet and its width is 4 feet. What is the area of the blackboard in square feet? What is its area in square yards?
2. A slate blackboard, 32 feet wide, extends across one end of a schoolroom and half way along the side. The room is 28 feet long and 24 feet wide. Find the number of square feet of slate in the blackboard. How much will this blackboard cost at 25 cents per square foot?
3. A blueberry patch 20 rods long and 12 rods wide yielded a profit of $450. Find the number of acres in the area of the berry patch and the profit per acre.
4. A city lot 150 feet long and 50 feet wide cost $2500. Find the number of square feet in the area of the lot and the cost per square foot.
6. The floor of a bathroom 8 feet 4 inches long and 6 feet 2 inches wide is covered with tiles an inch square. How many tiles were required to lay the floor?
6. An acre must contain 160 square rods. State the different dimensions which an acre may have. For example, it may be 16 rods long and 10 rods wide.
A square is a rectangle with equal sides. 7. A field is 40 rods square. How many acres are there in the field? If the yield of oats on this field was 650 bushels, what was the yield per acre?
It should be explained to the pupils that the principle on page 238 is used as a matter of custom and of convenience. Of course, there is really no such thing as “the product of its base and altitude,” since a multiplier must always be an abstract number. What is meant is that the number expressing the square units of a rectangle is equal to the number of units of its length multiplied by the number of units of its breadth. It is the abstract numbers that are multiplied together, and not the length and the breadth. This will apply to other similar statements.