Full resolution (JPEG) - On this page / på denna sida - Mensuration - To find the area of the slanted surface of a frustum of a pyramid - To find the total area of a frustum of a pyramid - To compute the volume of a frustum of a pyramid - To find the surface of a sphere
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MENSURATION. 207
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iffiastum <jf a Pyramid
To Find the Area of the Slanted
Surface of a Frustum of
a Pyramid.
Rule.
Add perimeter of the small end
to the perimeter of the large end.
Multiply this sum by the slant height
of the side (not slant height of edge).
Divide the product by 2.
To Find the Total Area of the Surface of a Frustum of a
Pyramid.
Rule.
Find the area of the slanted surface as explained above,
and to this area add the area of the two ends. Their areas are
obtained in the same way as areas of polygons. (See page 196).
To Compute the Volume of a Frustum of a Pyramid.
Rule.
Multiply the area of the small end by the area of the large
end, extract the square root of the product, and to this add the
area of the small end and the area of the large end ; multiply the
sum by one-third of the perpendicular height.
Formula
:
Volume
Example.
A (a + A +VA a)
Find volume of a frustum of a pyramid when the area of
the small end is 8 square feet, the area of the large end is 18
square feet and the perpendicular height is 30 feet.
30
Volume = v =
3
X (8 + I8+V18 X
2/ = i0X (8 + 18 + \/l44 )
v — 10 X ( 8 + IS + 12 )
v = 10 X 38
v = 380 cubic feet.
)
To Find the Surface of a Sphere.
Rule.
Multiply the circumference by the diameter.
Note.—The surface of a sphere is equal to the curved sur-
face of a cylinder having diameter and length equal to the
diameter of the sphere.
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