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EXAMPLES.

1. What is the area of a circle whose diameter is 6 ? We first square the diam

OPERATION. eter, giving 36, which we

62=36 then multiply by the decimal .7854 X 36=28.2744 .7854: the product is the Ans. 28.2744 area of the circle. 2. What is the area of a circle whose diameter is 10 ?

Ans. 78.54. 3. What is the area of a circle whose diameter is 7 ?

Ans. 4. How many square yards in a circle whose diameter is 31 feet?

Ans. 1.069016+. 287. A sphere is a solid ter

D minated by a curved surface, all the points of which are equally distant from a certain point within called the centre.

E

B The line AD passing through its centre C is called the diameter of the sphere, and AC its radius.

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288. To find the surface of a sphere, Multiply the square of the diameter by 3.1416.

EXAMPLES.

1. What is the surface of a sphere whose diameter is 12 ?

OPERATION. We simply multiply the

3.1416 decimal 3.1416 by the square

12=144 of the diameter: the product is the surface.

Ans. 452.3904

287. What is a sphere? What is a diameter? What is a radius?

288. How do you find the surface of a sphere ?

2. What is the surface of a sphere whose diameter is 7 ?

Ans. 153.9384. 3. Required the number of square inches in the sur. face of a sphere whose diameter is 2 feet or 24 inches.

Ans. 4. Required the area of the surface of the earth, its mean diameter being 7918.7 miles.

Ans. 196996571.722104 sq. miles.

289. To find the solidity of a sphere,

Multiply the surface by the diameter and divide the product by 6, the quotient will be the solidity.

EXAMPLES

1. What is the solidity of a sphere whose diameter is 12 ?

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2. What is the solidity of a sphere whose diameter is 4 ?

Ans. 33.5104. 3. What is the solidity of a sphere whose diameter is 14 inches ?

Ans. 4. What is the solidity of the earth, its mean diameter being 7918.7 miles ? Ans. 259992792079.860+.

5. What is the solidity of a sphere whose diameter is 6 feet ?

Ans. 113.0976 S. ft.

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289. How do you find the solidity of a sphore ?

290. A prism is a solid whose

K ends are equal plane figures and whose faces are parallelograms.

I The sum of the sides which bound the base is called the peri

H meter of the base, and the sum of the parallelograms which bound

E the solid is called the convex surface.

A To find the convex surface of a prism,

B С Multiply the perimeter of the base by the perpendicular height, and the product will be the convex surface.

EXAMPLES.

1. What is the convex surface of a prism whose base is bounded by five equal sides, each of which is 35 feet, the altitude being 26 feet ?

Ans. 4550 Sq.ft. 2. What is the convex surface when there are eight equal sides, each 15 feet in length, and the altitude is 12 feet ?

Ans. 1440 Sq. ft. 291. To find the solid content of a prism,

Multiply the area of the base by the altitude, and the product will be the content.

a

EXAMPLES.

1. What is the content of a square, prism, each side of the square which forms the base being 15, and the altitude of the prism 20 feet ?

We first find the area of the square which forms the base,

15°=225 and then multiply by the alti.

20 tude.

Ans. 4500

OPERATION.

290. What is a prism? What is the perimeter of its base? What is its convex surface? How do you find the convex surface of a prism?

291. How do you find the solid content of a prism?

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2. What is the solid content of a cube each side of which is 24 inches ?

Ans. 13824 solid in. 3. How many cubic feet in a block of marble of which the length is 3 feet 2 inches, breadth 2 feet 8 inches, and height or thickness 2 feet 6 inches? Ans. 21} solid ft.

4. How many gallons of water will a cistern contain whose dimensions are the same as in the last example ?

Ans. 1573} igal. 5. Required the solidity of a triangular prism whose height is 10 feet, and area of the base 350 ?' Ans. 3500.

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292. A cylinder is a round body with circular ends. The line EF is called the axis or altitude, and the circular surface the convex surface of the cylinder.

293. To find the convex surface,

Multiply the circumference of the base by the altitude, and the product will be the convex surface.

EXAMPLES.

1. What is the convex surface of a cylinder, the diameter of whose base is 20 and the altitude 50 ?

We first multiply the diame- OPERATION. ter by 3.1416, which gives the

3.1416 circumference of the base.

20 Then multiplying by the alti

62.8320 tude, we obtain the convex sur.

50 face.

Ans. 3141.6000

a

292. What is a cylinder? What is the axis or altitude ? What is the convex surface ? 293. How do you find the convex surface ?

2. What is the convex surface of a cylinder whose altitude is 14 feet and the circumference of its base 8 feet 4 inches ?

Ans. 116.666+ Sq.ft. 3. What is the convex surface of a cylinder, the diameter of whose base is 30 inches and altitude 5 feet?

Ans. 5654.88 Sq.in. 4. What is the convex surface of a cylinder, the diam. eter of whose base is 20 and altitude 50 feet ?

Ans. 3141.6 Sq. ft.

a

294. To find the solidity of a cylinder,

Multiply the area of the base by the altitude : the product will be the solid content.

:

EXAMPLES.

1. Required the solidity of a cylinder of which the altitude is 12 feet, and the diameter of the base 15 feet.

We first find the area of the base, and then multiply by the altitude : the product is the solidity.

OPERATION.
15°=225

.7854 176.7150

12 2120.5800

area base

2. What is the solidity of a cylinder, the diameter of whose base is 20 and the altitude 29 ? Ans. 9110.64.

3. What is the solidity of a cylinder, the diameter of whose base is 12 and the altitude 30 ? Ans. 3392.928.

4. What is the solidity of a cylinder, the diameter of whose base is 16 and altitude 9 ?

Ans. 5. What is the solidity of a cylinder, the diameter of whose base is 50 and altitude 15 ? Ans. 29452.5.

294. How do you find the solidity of a cylinder ?

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