answersLogoWhite

0

(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)

User Avatar

Wiki User

11y ago

What else can I help you with?

Continue Learning about Statistics

What is the average volume of a garbage can?

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.


Is large size bigger than medium size?

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.


How much blood should a woman 5ft 2in have in her body?

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.


How many m and ms are sold in a day?

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.


How much blood in a 150 lb male?

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.

Related Questions

What is the given volume of a rectangular pyramid?

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


What is a rectangular based pyramid with the top cut off?

It is a frustum of a rectangular pyramid.


Rectangular based pyramid?

I don't really understand your question, but one example of a rectangular based pyramid is the Great Pyramid in Giza.


What is a figure with four faces that are triangles and rectangle base?

In trigonometry, we call it a rectangular pyramid.


What is a rectangular based not square pyramid called?

A rectangle based pyramid!


What 3d shape has 7 sides?

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.


Which solid has one rectangular face?

a rectangular based pyramid


How many vertices does a rectangular pris have than rectangular pyramid?

A rectangular prism has 8 vertices whereas rectangular based pyramid has 5 vertices


How many faces has a triangular based prism pyramid have?

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.


How many vertices of a rectangular pyramid have?

A rectangular based pyramid has 5 vertices, 8 edges and 5 faces


What does a truncated octahedron look like?

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.


How do you work out the trigonometry of a rectangular based pyramid?

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.