To find the solidity of a cylinder.

Multiply the square of the diameter by the length; then multiply by II and divide by 14.

Ex. Find the solidity of a cylinder whose length is 4 ft. 8 in., and diameter 2 ft. 6 in.

CYLINDRICAL SHELL.

XXVIII.

To find the solidity of a cylindrical shell.

Multiply the sum of the inner and outer diameters by their difference, and this product by the length of the shell; then multiply by 11 and divide by 14.

Ex. Find the weight of a cast-iron pipe whose length is 9 feet, and the inner and outer diameters 6 and 8 inches.

EXAMPLES.

I. Find the curve surface of a cylinder whose length

is 9 ft. 4 in., and diameter 3 ft. 5 in.

Ans. 1003. sq. ft.

2. Find the curve surface of a cylinder whose length is 4 yards, and diameter 33 yards. Ans. 53 yards.

3. Find the cost of painting a cylindrical pillar whose length is 12 feet, and diameter 3 ft. 6 in., at 9d. per square yard. Ans. IIS.

4. Find the cost of covering a cylinder with felt at 6d. per foot, whose diameter is 2 ft. 4 in., and length 7 ft. 2 in. Ans. 1. 8s. 511d.

5. Find the solidity of a cylinder whose length is 10 ft. 6 in., and diameter 7 ft. 4 in. Ans. 4433 feet.

6. Find the number of gallons contained in a cylindrical vessel whose depth is 21 yards, and diameter 13 yards.

Ans. 1012 229.

7. A gallon of water weighs 10 lbs. Find the weight of water contained in a cylindrical vessel whose length is

5 ft. 3 in., and diameter 2 ft. 8 in.

Ans. 16 cwt. I qr. 8 lbs.

8. Find the weight of a cylindrical block of cast iron, whose diameter is 2 ft., and length 2 ft. 9 in.

Ans. 33 cwt. I qr. 9 lbs.

9. Find the solidity of a cylindrical shell whose inner and outer diameters are 33 and 37 inches, and length 6 feet. Ans. 9 feet.

10. Find the weight of a cast-iron pipe whose length is 9 feet; the inner and outer diameters being 3 and 4 inches. Ans. 2 cwt. 14 lbs.

To find the solidity of a pyramid.

Multiply the area of the base by the perpendicular height, and divide by 3.

Ex. Find the solidity of a triangular pyramid whose height is 36 feet, and the sides of the base 11, 13, 20 feet.

Area of base = 66

36

396

198

3 2376

792 Ans.

EXAMPLES.

I. The sides of the base of a triangular pyramid are 15 ft. 10 in., 19 ft. 3 in., 31 ft. 5 in., and the altitude 33 ft. 6 in.; find the solidity.

Ans. 136122 feet.

2. The base of a pyramid is a regular heptagon whose side is 9 ft. 3 in., and the altitude is 30 feet; find the solidity. Ans. 3109:34 feet.

3. The sides of the base of a triangular pyramid are 14 ft. 3 in., 16 ft. 6 in., 18 ft. 9 in., and the altitude 19 ft. 6 in.; find the solidity. Ans. 737.221 feet.

THE CONE.

This solid is formed by the revolution of a right-angled triangle about one of the sides containing the right angle. XXX.

To find the curve surface of a cone.

Multiply the diameter of the base by the slant side; then multiply by 11 and divide by 7.

Ex. Find the curve surface of a cone whose diameter is 7 ft. 4 in., and slant side 13 ft. 5 in.