Advanced Arithmetic

4. What is the area covered by the base of a circular kettle 15 inches in diameter? (Use 3.1416.)

5. At 11⁄2 cents a foot, how much will it cost to fence a circular bed of tulips if the distance across the bed is 56 inches? (Use 34.)

6. A farmer has a well 31⁄2 feet in diameter. the area of the opening? (Use 34.)

What is

7. Find the approximate area of the base of a circular chimney 35 feet in diameter; the exact area.

CYLINDER: SURFACE, VOLUME

Of what shape are the ends or bases of this solid? How do they compare in size? If the bases are equal and parallel, what is true of their diameters? What is true of the diameter of the whole solid?

A solid of uniform diameter whose bases are equal and parallel circles is a cylinder.

The altitude of a cylinder is the perpendic

ular distance between its bases.

The lateral or curved surface of a cylinder is the convex surface.

Exactly fit a piece of paper around a cylinder. What form has it when unrolled? How does the length of the rectangle compare with the circumference of the base? How does the width of the rectangle compare with the altitude of the cylinder? How

can the convex surface of a cylinder be found?

The convex surface of a cylinder is equal to the product of its circumference and its altitude.

The entire surface of a cylinder is equal to the sum of the convex surface and the areas of the bases.

1. What is the convex surface of a cylinder whose circumference is 14 in. and whose altitude is 3 ft.?

8. Find the entire surface of the above cylinders.

9. What is the convex surface of a stovepipe 7 in. in diameter and 3 ft. long?

10. A tin dish is 5 in. in diameter and 10 in. high. What is its entire outside surface?

11. What is the entire outside surface of a log 25 in. in diameter and 14 ft. long?

12. At 12 a square yard, how much will it cost to paint the convex surface of a silo 15 ft. in diameter and 24 ft. high?

If the base of this cylinder covers 2 sq. in., how many cubic inches are represented by a layer 1 in. high? How many cubic inches in the whole cylinder?

Tell how to find the volume of a cylinder.

The volume of a cylinder is found by multiplying the area of its base by its altitude.

7. Mr. Merriam has a silo 17.5 ft. in diameter and 25 ft. high. What is its capacity in cubic feet?

8. How many gallons of water will be required to fill a kettle whose diameter is 14 in. and whose height is 12 in.?

9. A water tank by the side of a railroad track is 12 ft. in diameter and 15 ft. high. Find its capacity in gallons.

10. A copper hot water boiler is 15 in. in diameter and 4 ft. high. How many square feet of copper were required to make it? What is the capacity of the boiler in gallons?

11. An iron ash can whose base covers 31 sq. ft. is 2 ft. 4 in. deep. Find its capacity.

PERCENTAGE

The expression per cent means by hundredths.

Oral

Thus, 3 per cent of a dollar means 3 hundredths, or .03, of a dollar.

The sign % means the same as the expression per cent. Thus, 7% of a dollar and 7 per cent of a dollar mean the same thing — 7 hundredths, or .07, of a dollar.

1. Into how many hundredths can a dollar be separated? A ton of coal? A yard of cloth? Anything?

PER CENT AND FRACTIONAL EQUIVALENTS 237

10 cents?

100 cents?

2. What per cent of a dollar is 1 cent? 25 cents? 50 cents? 75 cents? 80 cents? 3. What part of a whole thing is 1% of it? it? 25% of it? 50% of it? 75 % of it? 100 4. What per cent of a whole thing is of it? of it?of it? of it?

188 of it?

of it?

10% of

% of it?

of it?

5. A man bequeathed 60 % of his estate to his family, and the balance equally to four charitable institutions. What per cent of the estate to each institution?

6. A dealer in farm supplies sold of his stock of seeds in the spring, 25% in the summer, and the remaining part in the fall. What per cent in the fall?