Page:LA2-NSRW-5-0228.jpg



2212                                                            ARITHMETIC

Therefore, the area of a circle = \ the circumference multiplied by the radius.

Circumference = D X 3.1416 \ circumference = B X 3.1416

Substitute R X 3.1416 in the above. Area of circle = 3.1416 X R X B Area of circle = 3.1416 X R2 Area of circle^^R2 (the most convenient form to remember).

EXERCISE 44.

1.   The radius of a circle is 42 in. How many feet in its circumference ?

2.   What is the distance across a circular piece of ground which measures 57 rods around?

3.   Find how far a carriage has gone when one of its wheels, measuring 3 ft. 8 in. in diameter, has made 1600 revolutions.

4.   How long a piece of iron will a blacksmith require for the tire of wagon wheel 4| ft. in diameter, if 6 in. are allowed for welding!

5.   A horse is tied with a rope so that his head can reach 22 ft. from the stake in any direction. "What is the area of the ground over which he can graze?

6.   There are two circles drawn from the same center. The circumferences measure 132 ft. and 198 ft., respectively. Find the width of the ring formed by these two circles.

RULES FOR FINDING CURVED SURFACES.

1.   The convex surface of a prism is the product of the perimeter of its base by its altitude.

2.   The convex surface of a cylinder is the product of the circumference of its base by its altitude.

3.   The convex surface of a pyramid is one-half the product of the perimeter of its base by its slant height.

4.   The convex surface of a cone is one-half the product of the circumference of its base by its slant height.

5.   The surface of a sphere is four times the square of its radius times 3.1416.