Full resolution (JPEG) - On this page / på denna sida - Mensuration - To find the volume of a frustum of a cone - To find the area of the slanted surface of a pyramid - To find the total area of the surface of a pyramid - To find the volume of a pyramid
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2 06 MENSURATION.
To Find the Volume of a Frustum of a Cone.
Rule.
Square the largest radius ; square the smallest radius.
Multiply largest radius by smallest radius ; add these three pro-
ducts and multiply their sum by 3.1416 ; multiply this last
product by one-third of the perpendicular height.
Formula
:
Volume = (^+rHi?r)^A
Example.
Find the volume of a frustum of a cone. The largest
diameter is 6 feet, the smallest diameter is 4 feet, and perpen-
dicular height is 12 feet.
Solution
:
Volume — x— (3
2
+ 22
+ 3 X 2) X 3.1416 X —
o
x = (9 + 4 + 6) X 3.1416 X 4
x = 19 X 3.1416 X 4
x = 238.7616 cubic feet.
Note.—This rule will also apply for finding the solid con-
tents of wood in a log.
fig. 12.
To Find the Area of the slanted
_ ,–
^ Surface of a Pyramid.
/\ \ ( See Fig. 12).
// ! v\ & Rule.
//’/ !
V-\
l%
»
Multiply the length of the perim-
/// ’
\^\ ^ eter °^ tne base, by the slant height of
/ JJ.—)
r A\\\ \ the side (not the slant height of the
,^.1 ! LjA ^-’ edge). Divide the product by 2, and
>I X-—i’ the quotient is the area.
Pyramid
To Find the Total Area of the Surface of a Pyramid.
Rule.
Find area of the slanted surface as explained above, and to
this add the area of a polygon equal to the base of the pyramid.
To Find the Volume of a Pyramid.
Rule.
Multiply the area of the base by one-third of the perpen-
dicular height.
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