Full resolution (JPEG) - On this page / på denna sida - Mensuration - Area of a circle - To change a circle into a square of the same area - To find the side of the largest square which can be inscribed in a circle - To find the area of any irregular figure
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MENSURATION. 197
Therefore, according to the formulas,
the area of a triangle
base X perpendicular height
the area of a circle must be = circumference X radius
2
and from this follow all the other formulas.
To Change a Circle into a Square of the Same Area.
Rule.
Multiply the diameter of the circle by the constant 0.8862
and the product is the length of one side in a square of the same
area.
Example.
A circular water-tank 5 feet in diameter and 3 feet high is
to be replaced by a square tank of the same height and volume.
How long will each side in the new tank be?
Solution
:
Side = 5 X 0.8862 = 4.431 feet long.
To Find the Side of the Largest Square which can be
Inscribed in a Circle.
Rule.
Multiply the diameter of the circle by the constant 0.7071
;
the product is the length of the side of the square.
Example.
What is the largest square beam which can be cut from a
log 30 inches in diameter.
Solution
:
30 X 0.7071 = 21.213 inches square.
Note.—A round log of any diameter will always cut into a
square beam having sides seven-tenths the diameter of the
round log. For instance, a 10-inch log will cut 7 inches square,
a 15-inch log will cut 10.5 inches square, a 20-inch log will cut
14 inches square, etc.
Fig.
To Find the Area of Any Irregular Figure
(See Fig. 5).
Divide the figure into any
number of equal parts, as shown
by the perpendiculars 1, 2, 3, etc.
Measure the width of the figure
at the middle of each division
;
add these measurements together, «
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