To find the solidity of the frustum of a cone.

Add the squares of the diameters of the two ends and their product together; multiply the sum by the height of the frustum; then multiply by 11 and divide by 42.

Ex. Find the solidity of the frustum of a cone whose top and bottom diameters are 9 and 16 inches, and the depth 14 inches.

92= 81 162=256

9 × 16 = 144

EXAMPLES.

I. Find the solidity of a cone whose diameter is 10 yards, and altitude 111 yards. Ans. 324 yards.

2. Find the solidity of a cone whose diameter is 7 ft. 11 in., and slant side 16 ft. 1 in.

Ans. 255-879 feet.

3. Find the solidity of a cone whose diameter is 13 ft. 6 in., and slant side 18 ft. 4 in.

Ans. 813.7.2 feet.

4. Find the solidity of the frustum of a cone whose top and bottom diameters are 4 and 71 feet, and the depth 8 feet. Ans. 220.1I feet. 5. Find the solidity of the frustum of a cone whose top and bottom diameters are 18 ft. 5 in., and 13 ft. 1 in., and slant side 21 ft. 5 in. Ans. 4181.4 feet. 6. The top and bottom diameters of a tub are 4 ft. 3 in. and 2 ft. 9 in., and the depth 4 ft. 10 in.; how many gallons will it hold? Ans. 294.

7. Find the weight of a conical plug of cast iron whose diameter is 9 inches, and height 15 inches.

Ans. 79 lbs.

8. The sides of a right-angled triangle are 1 ft., 2 ft. 11 in., 3 ft. 1 in.; if it revolve about the hypothenuse, find the solidity and surface of the solid.

Ans. 283 feet, 11143 feet.

THE SPHERE.

O

This solid is formed by the revolution of a circle about

meter,

XXXIV.

To find the surface of a sphere.

Multiply the square of the diameter by 3

Ex. Find the surface of a sphere whose diameter is

To find the curve surface of the segment of a sphere.

(1) When the diameter of the sphere and the height of the segment are given: Multiply the diameter of the sphere by the height of the segment; then multiply by 3

Ex. The diameter of a sphere is 6 ft. 5 in.; find the area of a segment whose height is 2 ft. 6 in.

(2) When the dimensions of the segment are given: Multiply the sum of the squares of the radius and the depth of the segment by 3

Ex.

Find the curve surface of the segment of a sphere whose radius is 7 ft. 7 in., and depth 5 ft. 3 in.

Given the surface of a sphere to find the diameter.

Multiply the surface by 7 and divide by 22; then extract the square root.

I.

Find the surface of a sphere whose diameter is
Ans. 240 feet.

8ft. 9. in.

2. Find the cost of painting a globe whose diameter is 56 in., at Is. 2d. per square foot. Ans. £3. 195. 103d.

3. The diameter of a sphere is 8 ft. 9 in.; find the curve surface of a segment whose height is 2 ft. 7 in.

Ans. 71 feet.

4. Find the diameter of a sphere whose curve surface is 6734 square feet.

Ans. 46 288 ft.

5. Find the surface of a sphere whose diameter is 121 Ans. 491 yards.

yards.