(1)
Best formula to use is as follows -
V = h/3(Areatop + √(Areatop*Areabottom) + Areabottom)
(2)
To find (h) using a tape measure -
Areatop => bd
Areabase => ac
Lateral edge remaining => e (from top corner to base corner)
k = 1 - √(bd/ac)
H= √([e/k]² - [a/2]² - [c/2]²)
h = Hk
V = H/3*(ac-bd+bd*k)
(3)
Lets say Top is a rectangle with sides b & d
and bottom is a rectangle with sides a & c respectively.
Let height be h
in that case the volume of Truncated Pyramid with rectangular base will be -
V = 1/3((a²c-b²d)/(a-b))h
BUT BE CAREFUL - a,b,c,d are not all independent variables (one depends on the others) so this answer is misleading!!!
Proof -
Suppose the height of Full Pyramid is H
From parallel line property
(H-h)/H = b/a
Rearranging
H = ah/(a-b) --------------------(1)
Also
Since V=1/3 Base area X Height
Volume of full pyramid = 1/3 X ac X H
Volume of removed Pyramid = 1/3 X bd X (H-h)
So volume of truncated part V = 1/3(acH-bd(H-h))
=1/3((ac-bd)H + bdh)
From (1)
V = 1/3((ac-bd)ah/(a-b) + bdh)
reducing and rearranging we get
V = 1/3((a²c-b²d)/(a-b))h
(4)
In case the truncated solid forms a prism instead, we have following formula -
V = ( h/6)(ad + bc + 2ac + 2bd)
Proof -
Fig(1)
Fig(2)
Lets divide the fig(1) into four different shapes as shown in fig(2)
VA = Volume of cuboid = bdh
VB = Volume of prism after joining both Bs= ½ X base X height X width = ½ (a-b) (d)(h)
VC = Volume of prism after joining both Cs = ½ X base X height X width = ½ (c-d) (b)(h)
VD = Volume of rectangular pyramid after joining all Ds = 1/3 X base area X height =
1/3 (a-b) (c-d) h
Then V = VA + VB + VC + VD
Or, V = bdh + 1/2(a-b)dh +1/2(c-d)bh + 1/3(a-b)(c-d)h
Arranging and simplifying we get -
V = ( h/6)(ad + bc + 2ac + 2bd)
The average volume of a residential garbage can typically ranges from 20 to 96 gallons, with 32-gallon and 64-gallon sizes being the most common. For commercial use, garbage cans can vary more widely, often holding anywhere from 32 gallons to several hundred gallons, depending on the needs of the establishment. The volume can also differ based on local regulations and waste management practices.
Yes, large size is bigger than medium size. Sizes are typically arranged in an order where small is the smallest, followed by medium, and then large as the largest option. This hierarchy helps in categorizing items based on their dimensions or volume.
The average blood volume in an adult is approximately 70 milliliters per kilogram of body weight. For a woman who is 5 feet 2 inches tall, her weight can vary, but if we assume an average weight of around 130 pounds (59 kg), she would typically have about 4 to 5 liters of blood in her body. Individual blood volume can vary based on factors such as body composition and overall health.
On average, about 400 million M&M's are sold each day worldwide. This figure can vary based on factors like seasonality and special promotions. The popularity of M&M's as a snack and their use in various recipes contribute to their high sales volume.
A typical adult male has about 1.2 to 1.5 gallons of blood, which is roughly 10-12 pints. For a 150 lb male, this translates to approximately 5.5 to 6.5 liters of blood. This volume can vary based on factors like body composition and overall health.
The volume of any pyramid or cone is given by the formula: 1/3 x base area x height For a rectangular-based pyramid: 1/3 x base width x base length x height
It is a frustum of a rectangular pyramid.
I don't really understand your question, but one example of a rectangular based pyramid is the Great Pyramid in Giza.
In trigonometry, we call it a rectangular pyramid.
A rectangle based pyramid!
A heptahedron.There are 34 distinct heptahedra: some of these are:a hexagon based pyramid,a pentagon based pyramid with one of the basal vertices truncated,a cuboid with one of its vertices truncated.
a rectangular based pyramid
A rectangular prism has 8 vertices whereas rectangular based pyramid has 5 vertices
five A triangular based prism has 5 A triangular based pyramid has 4 and there is no such thing as a triangular based prism pyramid - unless you mean a truncated pyramid (or a frustum) which is essentially a prism.
A rectangular based pyramid has 5 vertices, 8 edges and 5 faces
You start with a quadrilateral based bipyramid, which has six vertices. At each vertex, remove the tip in the form of a quadrilateral based pyramid. You will be left with a truncated octahedron.
The answer depends on what you wish to work out: the angles, height, surface area, volume. Also, you need more information: the vertical or inclined height and whether or not the pyramid is a right pyramid.