(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)
Chat with our AI personalities
a estimate is based on known information it is just not a true answer.
IQ is not based on age, it's based on intelligence.
Qualitative is the grouping of things based on their qualities. Quantitative is based off of the quantity, or amount there is, of something.
The probability based on an event that has already occurred is 100%. If the event has occurred, it has occurred.
No. Outliers are part of the data and do not affect them. They will, however, affect statistics based on the data and inferences based on the data.