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fo. What is the side of that equilateral triangle, whose area cost as much for paving at 8d. sterling a foot, as the pallisading of the three sides did at a guinea a yard ? Ans. 72746 feet.

11. A roof, which is 24 feet 8 inches by 14 feet 6 inches, is to be covered with lead, at 81b. to the square foot; what will it come to, at 18s. per cwt. ?

Ans. 221. 195. 101d.

12. Having a rectangular marble slab, 8 inches by 27, I would have a square foot cut off parallel to the shorter edge; I would then have the like quantity divided from the remainder parallel to the longer side; and this alternately repeated, till there shall not be the quantity of a foot left; what will be the dimensions of the remaining piece? Ans. 2017 inches by 6·086.

13. If from a right-angled triangle, whose base is 12 and perpendicular 16 feet, a line be drawn parallel to the perpendicular cutting off a triangle, whose area is 24 square feet; required the sides of this triangle.

Ans. 6, 8, and 10.

14. If a round pillar 7 inches over, have 4 feet of stone in it; of what diameter is the column of equal length, that contains 10 times as much? Ans. 22°136 inches.

15. The area of an equilateral triangle, whose base falls on the diameter, and its vertex in the middle of the arc of a semicircle, is equal to 100; what is the diameter of the semicircle ? Ans. 26 32148.

16. It is required to find the thickness of the lead in a pipe of an inch and a quarter bore, which weighs 14lb. per yard in length; the cubic foot of lead weighing 11325 Ans. 20737 inches.

ounces.

17. What

17. What is the length of a chord, which cuts off of the area of a circle, whose diameter is 289 ?

Ans. 278.6716.

18. What will the diameter of a globe be, when the solidity and superficial content are expressed by the same number?: : Ans. 6.

19. A sack, that will hold 3 bushels of corn, is 22 inches broad, when empty; what will that sack contain, which, being of the same length, has twice its breadth or circumference ? Ans. 12 bushels.

1

20. A carpenter is to put an oaken curb to a round well, at 8d. per foof square; the breadth of the curb is to be 7 inches, and the diameter within 13 feet; what will be the expense? Ans. 55. 24d.

21. A gentleman has a garden 100 feet long and 80 feet broad, and a gravel walk is to be made of an equal width half round it; what must the breadth of the walk be to take up just half the ground?

Ans. 25'968 feet.

22. Seven men bought a grinding stone of 60 inches diameter, each paying part of the expense; what part of the diameter must each grind down for his share? Ans. The 1st, 4'4508,

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23. A maltster has a kiln, that is, 16 feet 6 inches square; but he wants to pull it down and build a new

one,

one, that will dry 3 times as much at once as the old one; what must be the length of its sides?

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24. How many 3 inch cubes may be cut out of a 12 inch cube? Ans. 64.

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125. What will the painting of a conical spire come to, at 8d. per yard; supposing the height to be. 118 feet, and the circumference of the base 64 feet? Ans. 141. 8d.

26. The diameter of a standard corn bushel is 18 inches, and its depth 8 inches: what must the diameter of that bushel be, whose depth is inches?

Ans. 19°1067.

27. To divide a cone into three equal parts by sections parallel to the base, and to find the altitudes of the three parts; the height of the whole cone being 20 inches.

Ans. The upper part 13.867.
The middle part 3.604.*

The lower part 2.528.

28. A gentleman has a bowling green 300 feet long andˇ200 feet broad, which he would raise one foot higher by means of the earth to be dug out of a ditch, that goes round it to what depth must the ditch be dug, supposing its breadth to be every where 8 feet ?

Ans. 7 feet.

29. How high above the earth must a person be raised, that he may see of its surface?

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Ans. To the height of the earth's diameter.

30. A cubic foot of brass is to be drawn into a wire of of an inch in diameter: what will the length of the wire be, allowing no loss in the metal ?

Ans. 97784 797 yards, er 55 miles 9S4 797 yards.

31. If a heavy sphere, whose diameter is 4 inches, be let fall into a conical glass full of water, whose diameter is 5, and altitude 6 inches; it is required to determine how much water will run over.

Ans. 26-272 cubic inches, or nearly

parts of a pint.

32. The dimensions of the sphere and cone being the same as in the last question, and the cone only full of water; required what part of the axis of the sphere is im mersed in the water.

Ans. 546 parts of an inch.

733. The cone being still the same, and full of water; required the diameter of a sphere, which shall be just covered by the water.

Ans. 2'445996.

TABLE

TABLE

OF THE AREAS OF THE SEGMENTS OF A CIRCLE, WHOSE DIAMETER IS UNITY, AND SUPPOSED TO BE

DIVIDED INTO 1000 EQUAL PARTS.

Height

Area Seg. Height. Area Seg. Height. Area Seg.

.001

⚫000042

029

006527

057

017831

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030 006865

058

018296

003

⚫000219 ·031 •007209

059

018766

[blocks in formation]

060

019239

·005

•000470 033

007913

.061

019716

·006 .000618 034

[blocks in formation]

*007 •000779 035

008638

063

020680

•008

•000951 036

[blocks in formation]

021168

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