Height of Ingot given Space Diagonal Solution

STEP 0: Pre-Calculation Summary
Formula Used
Height of Ingot = sqrt(Space Diagonal of Ingot^2-((Larger Rectangular Length of Ingot+Smaller Rectangular Length of Ingot)^2)/4-((Larger Rectangular Width of Ingot+Smaller Rectangular Width of Ingot)^2)/4)
h = sqrt(dSpace^2-((lLarge Rectangle+lSmall Rectangle)^2)/4-((wLarge Rectangle+wSmall Rectangle)^2)/4)
This formula uses 1 Functions, 6 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Height of Ingot - (Measured in Meter) - Height of Ingot is the vertical distance between the top and bottom rectangular faces of the Ingot.
Space Diagonal of Ingot - (Measured in Meter) - Space Diagonal of Ingot is the distance between one corner of top rectangular face and the diagonally opposite corner of the bottom rectangular face of the Ingot.
Larger Rectangular Length of Ingot - (Measured in Meter) - Larger Rectangular Length of Ingot is the length of the longer pair of opposite sides of the larger rectangular face of the Ingot.
Smaller Rectangular Length of Ingot - (Measured in Meter) - Smaller Rectangular Length of Ingot is the length of the longer pair of opposite sides of the smaller rectangular face of the Ingot.
Larger Rectangular Width of Ingot - (Measured in Meter) - Larger Rectangular Width of Ingot is the length of the shorter pair of opposite sides of the larger rectangular face of the Ingot.
Smaller Rectangular Width of Ingot - (Measured in Meter) - Smaller Rectangular Width of Ingot is the length of the shorter pair of opposite sides of the smaller rectangular face of the Ingot.
STEP 1: Convert Input(s) to Base Unit
Space Diagonal of Ingot: 56 Meter --> 56 Meter No Conversion Required
Larger Rectangular Length of Ingot: 50 Meter --> 50 Meter No Conversion Required
Smaller Rectangular Length of Ingot: 20 Meter --> 20 Meter No Conversion Required
Larger Rectangular Width of Ingot: 25 Meter --> 25 Meter No Conversion Required
Smaller Rectangular Width of Ingot: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
h = sqrt(dSpace^2-((lLarge Rectangle+lSmall Rectangle)^2)/4-((wLarge Rectangle+wSmall Rectangle)^2)/4) --> sqrt(56^2-((50+20)^2)/4-((25+10)^2)/4)
Evaluating ... ...
h = 40.0593309979086
STEP 3: Convert Result to Output's Unit
40.0593309979086 Meter --> No Conversion Required
FINAL ANSWER
40.0593309979086 40.05933 Meter <-- Height of Ingot
(Calculation completed in 00.004 seconds)

Credits

Created by Shweta Patil
Walchand College of Engineering (WCE), Sangli
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Verified by Mridul Sharma
Indian Institute of Information Technology (IIIT), Bhopal
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4 Height of Ingot Calculators

Height of Ingot given Skewed Edge Length
Go Height of Ingot = sqrt(Skewed Edge Length of Ingot^2-((Larger Rectangular Length of Ingot-Smaller Rectangular Length of Ingot)^2)/4-((Larger Rectangular Width of Ingot-Smaller Rectangular Width of Ingot)^2)/4)
Height of Ingot given Space Diagonal
Go Height of Ingot = sqrt(Space Diagonal of Ingot^2-((Larger Rectangular Length of Ingot+Smaller Rectangular Length of Ingot)^2)/4-((Larger Rectangular Width of Ingot+Smaller Rectangular Width of Ingot)^2)/4)
Height of Ingot given Slant Height at Rectangular Widths
Go Height of Ingot = sqrt(Slant Height at Rectangular Widths of Ingot^2-((Larger Rectangular Length of Ingot-Smaller Rectangular Length of Ingot)^2)/4)
Height of Ingot given Slant Height at Rectangular Lengths
Go Height of Ingot = sqrt(Slant Height at Rectangular Lengths of Ingot^2-((Larger Rectangular Width of Ingot-Smaller Rectangular Width of Ingot)^2)/4)

Height of Ingot given Space Diagonal Formula

Height of Ingot = sqrt(Space Diagonal of Ingot^2-((Larger Rectangular Length of Ingot+Smaller Rectangular Length of Ingot)^2)/4-((Larger Rectangular Width of Ingot+Smaller Rectangular Width of Ingot)^2)/4)
h = sqrt(dSpace^2-((lLarge Rectangle+lSmall Rectangle)^2)/4-((wLarge Rectangle+wSmall Rectangle)^2)/4)

What is Ingot?

A polyhedron shaped like an Ingot is made of two regularly opposite, parallel rectangles. These have the same ratio of length and width and are connected at their corners. It has 6 faces (2 rectangles, 4 isosceles trapezoids), 12 edges and 8 vertices.

How to Calculate Height of Ingot given Space Diagonal?

Height of Ingot given Space Diagonal calculator uses Height of Ingot = sqrt(Space Diagonal of Ingot^2-((Larger Rectangular Length of Ingot+Smaller Rectangular Length of Ingot)^2)/4-((Larger Rectangular Width of Ingot+Smaller Rectangular Width of Ingot)^2)/4) to calculate the Height of Ingot, Height of Ingot given Space Diagonal formula is defined as the vertical distance between the top and bottom rectangular faces of the Ingot, calculated using its space diagonal. Height of Ingot is denoted by h symbol.

How to calculate Height of Ingot given Space Diagonal using this online calculator? To use this online calculator for Height of Ingot given Space Diagonal, enter Space Diagonal of Ingot (dSpace), Larger Rectangular Length of Ingot (lLarge Rectangle), Smaller Rectangular Length of Ingot (lSmall Rectangle), Larger Rectangular Width of Ingot (wLarge Rectangle) & Smaller Rectangular Width of Ingot (wSmall Rectangle) and hit the calculate button. Here is how the Height of Ingot given Space Diagonal calculation can be explained with given input values -> 40.05933 = sqrt(56^2-((50+20)^2)/4-((25+10)^2)/4).

FAQ

What is Height of Ingot given Space Diagonal?
Height of Ingot given Space Diagonal formula is defined as the vertical distance between the top and bottom rectangular faces of the Ingot, calculated using its space diagonal and is represented as h = sqrt(dSpace^2-((lLarge Rectangle+lSmall Rectangle)^2)/4-((wLarge Rectangle+wSmall Rectangle)^2)/4) or Height of Ingot = sqrt(Space Diagonal of Ingot^2-((Larger Rectangular Length of Ingot+Smaller Rectangular Length of Ingot)^2)/4-((Larger Rectangular Width of Ingot+Smaller Rectangular Width of Ingot)^2)/4). Space Diagonal of Ingot is the distance between one corner of top rectangular face and the diagonally opposite corner of the bottom rectangular face of the Ingot, Larger Rectangular Length of Ingot is the length of the longer pair of opposite sides of the larger rectangular face of the Ingot, Smaller Rectangular Length of Ingot is the length of the longer pair of opposite sides of the smaller rectangular face of the Ingot, Larger Rectangular Width of Ingot is the length of the shorter pair of opposite sides of the larger rectangular face of the Ingot & Smaller Rectangular Width of Ingot is the length of the shorter pair of opposite sides of the smaller rectangular face of the Ingot.
How to calculate Height of Ingot given Space Diagonal?
Height of Ingot given Space Diagonal formula is defined as the vertical distance between the top and bottom rectangular faces of the Ingot, calculated using its space diagonal is calculated using Height of Ingot = sqrt(Space Diagonal of Ingot^2-((Larger Rectangular Length of Ingot+Smaller Rectangular Length of Ingot)^2)/4-((Larger Rectangular Width of Ingot+Smaller Rectangular Width of Ingot)^2)/4). To calculate Height of Ingot given Space Diagonal, you need Space Diagonal of Ingot (dSpace), Larger Rectangular Length of Ingot (lLarge Rectangle), Smaller Rectangular Length of Ingot (lSmall Rectangle), Larger Rectangular Width of Ingot (wLarge Rectangle) & Smaller Rectangular Width of Ingot (wSmall Rectangle). With our tool, you need to enter the respective value for Space Diagonal of Ingot, Larger Rectangular Length of Ingot, Smaller Rectangular Length of Ingot, Larger Rectangular Width of Ingot & Smaller Rectangular Width of Ingot and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Height of Ingot?
In this formula, Height of Ingot uses Space Diagonal of Ingot, Larger Rectangular Length of Ingot, Smaller Rectangular Length of Ingot, Larger Rectangular Width of Ingot & Smaller Rectangular Width of Ingot. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Height of Ingot = sqrt(Skewed Edge Length of Ingot^2-((Larger Rectangular Length of Ingot-Smaller Rectangular Length of Ingot)^2)/4-((Larger Rectangular Width of Ingot-Smaller Rectangular Width of Ingot)^2)/4)
  • Height of Ingot = sqrt(Slant Height at Rectangular Widths of Ingot^2-((Larger Rectangular Length of Ingot-Smaller Rectangular Length of Ingot)^2)/4)
  • Height of Ingot = sqrt(Slant Height at Rectangular Lengths of Ingot^2-((Larger Rectangular Width of Ingot-Smaller Rectangular Width of Ingot)^2)/4)
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