2. Find the cost of 32 blocks of marble each 21 ft. by 2 ft. by 1 ft. at $1.75 per cubic foot.

3. How many loads of gravel will be required for a road 3 mi. long if spread 9 ft. wide and 8 in. deep?

4. A pile of tanbark is 27 yd. long, 12 ft. high, and 16 ft. wide. What is it worth at $7.20 a cord?

5. A business block is to be erected with a frontage of 40 ft. on Main Street and 48 ft. upon Seneca Street. The other measurements are as shown in the diagram. Find the cost of excavation to a depth of 12 ft. at 30¢ a load.

Lesson No. 7. Estimates involving Solids and Volumes

EXERCISES

1. Three-foot wood is piled 8 ft. high. How long should the pile be to contain 12 cords?

2. How many cut stones, each 9 in. long by 4 in. wide and 5 in. deep, will it take to pave a street 66 ft. wide and a half-mile long?

3. What weight of water will a rectangular tank contain, the length being 5 ft., the breadth 4 ft., and the depth 16 ft.? (A cubic foot of water weighs 62 lb.)

4. Find the cost of digging a ditch 2 mi. long by 14 ft. wide and 6 ft. deep at 35¢ a load.

80 ft.

180 feet

120 feet

5. An office building is to be of the dimensions shown in the above diagram. to a depth of 15 ft. the surface area as the depth.)

The cellar excavations are to be made Find the cost at 27 a load. (Find shown in Lesson 5; then multiply by

Lesson No. 8. Lumber and Timber Measurements

A foot of lumber, as the term is generally used, means a piece of board one foot square and one inch thick, or of an equivalent number of cubic inches (144) of wood in some other shape. When lumber is so measured the result is frequently spoken of as "board measure," or B. M.

To find the number of feet of lumber in a board or plank, that is, the number of feet "board measure," multiply the length in feet by the width and thickness in inches, and divide the product by 12.

If the boards are 12 ft. long and 1 in. thick, the width in inches represents the number of board feet.

To find the number of feet of lumber in a floor, or sidewalk, or fence, or platform, or any rectangular surface, multiply the length in feet by the breadth in feet, and if more than 1 in. thick, multiply by the thickness in inches.

EXERCISES

1. How many feet of lumber in a plank 18 ft. long by 18 in. wide and 2 in. thick?

2. How many feet of lumber in a stick of timber 24 ft. long and 18 in. square?

3. Find the cost of the lumber necessary for a floor 20 ft. by 18 ft. at $25 per thousand feet.

4. Find the value of 26,340 ft. of lumber at $27.50 per thousand.

5. A railway station is 64 ft. by 48 ft. The platform surrounding it is 16 ft. wide and is built of 2-in. plank. Find the value of the lumber used at $30 per thousand feet.

Lesson No. 9. Areas of Trapezoids

If two sides of a four-sided figure are parallel, the area can easily be found if we know the perpendicular distance between the parallel sides. Four-sided figures that have two opposite sides parallel are called trapezoids.

Suppose that we desire to find the area in square feet of the figure ABCD. We form the three rectangles as shown, and then find the area separately of the rectangles. Only half in each instance of the rectangles AGCE and FDHB would be taken in finding the total area.

Notice that the figure ACDB is the same in area as the rectangle EGHF. To find the length EF we add the lengths of AB and CD together and take half their sum. EF is the average length of AB and CD.

Now to find the area of a four-sided figure two sides of which are parallel, we multiply the average length of the parallel sides by the perpendicular distance between them.

EXERCISES

1. Find the area of a four-sided figure having two sides parallel. The lengths of the parallel sides are 12 ft. and 9 ft., respectively, and the perpendicular distance between them is 14 ft.

2. Find the cost of an inlaid wood floor the shape of the figure described above. AB is 28 ft. and CD is 18 ft. The floor is 15 ft. wide. The price is to be 18 a square foot. J

: L.......

3. Two city blocks are of the shape A and B shown in the figure. A has a frontage of 140 yd. on First Street, and 60 yd. on Second Street. B has a frontage of 24 yd. on First Street, 104 yd. on Second Street. The distance between First Street and Second Street is 272 ft. Find the total value of

the land in A and B at 3¢ a square foot.

the

4. Find the cost of paving Elm Street from E to F, street being 60 ft. wide, measured parallel with First or