...the cylinder ; find also, the capacity of the pump, supposing it to be similar to the cylinder. Since circles are to each other as the squares of their diameters, the area of the air-pump bucket is £th that of the piston. Hence its area = =1486 - 1675 square inches,...

...circle is 4 ft, its area will equal 4" X «.141« ,,.::.:>,-. 3.1410 sq. ft - 50.2656 sq. ft f z. ) The areas of circles are to each other as the squares of their diameters or of their radii. ILLUSTRATION. — The area of a circle 6 ft in diameter is 4 times the area of a...

...these will convey no more blood than the single trunk. For, according to a simple rule in geometry, the areas of circles are to each other as the squares of their diameters. The area of the trunk is expressed, therefore, by the square of 10-1, which is almost exactly 102. The...

...contains a greater area than any other plane figure, bounded by an equal perimeter, or outline. 2. The areas of circles are to each other as the squares of their diameters ; any circle twice the diameter of another contains four times the area of the other. 3. The diameter...

...to force water into a large cylinder, the piston of which is moved by the force transmitted. Now, as areas of circles are to each other as the squares of their diameters, it is plain that if the diameter of the plunger be one inch, and that of the piston 30 inches, a force...

...perimeter, or outline. 2. Circumference=3'1415926 of diameter. 3. Diameter = 0'31831 of circumference. 4. Areas of circles are to each other as the squares of their diameters , .( square of diameter x 7854. I square of circumference x '07958. 6. Diameter = square root of area...

...by the same figures that indicate the ratio of the circumference to the diameter. 4.77. Now, since the areas of circles are to each other as the squares of their diameters, or as the squares of their radii (330, 5), we have from the two preceding examples, To find the area...

...to grind down, the waste hole, through which the spindle passes, being 5 inches square ? NOTE 4. — The areas of circles are to each other, as the squares of their diameters. Ans. 6-675949 in., A grinds ; 10-310898 in., B grinds ; 11-942086 in., C grinds. 85. Divide $90, so...

...find that, 2772 — — - = 77 inches, 36 nearly equal to the area of the pump's bore ; now the area of circles are to each other as the squares of their diameters, and the area of a circle whose diameter is 9, is 63-6: therefore, 63-6 : 77 : : 9" : 98, the square...

...with 46-02, or just over 46 inches. Now, remembering the relations of similar figures, we know that circles are to each other as the squares of their diameters ; the square of the diameter of 6 circular gallons should therefore be 6 times the square of 1 circular gallon;...