An introduction to linear drawing/Chapter 13
SECTION III.
OF VOLUME.
Problem I. To find the volume of a prism or cylinder.
Rule. Multiply the base by the height, and the product will be the number of cubes (that is, solid squares) contained in the body.
Note. The length, breadth, and height, must always be expressed in the same sort of measure, whether it be yards, feet, or inches; if they are not so expressed in the proposition, they must be reduced before any thing else is done.
Example 1. A wall is 2,8 yards high ; 0,6 thick ; and 104,5 yards long ; how many cubick feet does it contain ?
2,8 multiplied by 0,6—gives 1,68 square yds. 1,68 multiplied by 104,5—gives 175,560 square yds.
2. A pile of wood in the form of a parallelopiped, is 54,8 feet long ; 22,3 feet wide ; and/ 37,1 feet in height ; how many cubick feet does it contain ?
Multiply these three numbers together, and the an- swer will be 45337,684 cubick feet.
8. A cylindrical caldron is 8,3 feet deep, and 13 feet wide ; what is its capacity (that is, how many cu- bick feet will it contain ?)
The width or diameter is 13, the radius must be 6,5. Multiply 6,5 by 6,5 and the product by 3} (Sect. II. Prob. 6,) and you have the superficies of the base, which multiply by the height 8,3 and you have the capacity required. Ans. 1102,124 cubick feet. 4. A common brick is generally 8 inches long, 4 wide, and two thick. What is its volume ? How many will it take to make a cubick foot of masonry ?
Ans. Vol. 64 sq. in. Cubick foot 27 bricks.
5. How many bricks will it take to construct a wall, 300 feet long, 6 feet high, and 1,5 thick ?
Note. It will be seen that this and the preceding cal- culation make no allowance for mortar.
6. A well is 6,9 yards deep, and 1,2 yards in diam- eter. I wish to make a wall in it, 0,4 yards thick ; how many cubick feet of stone will build it ?
Calculate the well as if it were to be entirely filled up. Its diameter being 1,2, its radius must be half that, or 0,6 tenths ; to this add, 0,4 tenths, the proposed thickness of the wall, and you have 10 tenths, or a whole yard, for the radius of the well.
Then subtract the empty part of the well, which forms another cylinder, whose radius is 0,6 tenth, as above mentioned.
1 m 1' " 1 1 * and by 3f gives 3,14 the base of the
0,6 multiplied by 6 and by 3y gives 1,13 for the base of the smaller cylinder, which subtracted from 3,14 leaves 2,01 which multiplied by the height, gives the answer. Ans. 13,869 square yards.
7. How many bricks would the above wall require ?
Rule. Take the superficies of the base, and twice that of the centre at the bung hole, (Prob. 3, Sect. I.) add the two amounts, and multiply the product by a third of the length.
Note. All these measurements should be of the in- side or Qlear, otherwise the thickness of the wood will be included.
Ans. 72900.
Ans. 10110,5
Problem ii. to gauge a cask.