Space Diagonal of Cuboid given Lateral Surface Area, Width, and Height Calculator

✖The Lateral Surface Area of Cuboid is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Cuboid.ⓘ Lateral Surface Area of Cuboid [LSA]			+10% -10%
✖The Height of Cuboid is the vertical distance measured from base to the top of Cuboid.ⓘ Height of Cuboid [h]			+10% -10%
✖The Width of Cuboid is the measure of any one of the pair of parallel edges of base which are smaller than the remaining pair of parallel edges of Cuboid.ⓘ Width of Cuboid [w]			+10% -10%

✖The Space Diagonal of Cuboid is the length of the line connecting one vertex to the opposite vertex through the interior of the Cuboid.ⓘ Space Diagonal of Cuboid given Lateral Surface Area, Width, and Height [d_Space]

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Space Diagonal of Cuboid given Lateral Surface Area, Width, and Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Space Diagonal of Cuboid = sqrt((Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Width of Cuboid)^2+Width of Cuboid^2+Height of Cuboid^2)
d_Space = sqrt((LSA/(2*h)-w)^2+w^2+h^2)
This formula uses 1 Functions, 4 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

Space Diagonal of Cuboid - (Measured in Meter) - The Space Diagonal of Cuboid is the length of the line connecting one vertex to the opposite vertex through the interior of the Cuboid.
Lateral Surface Area of Cuboid - (Measured in Square Meter) - The Lateral Surface Area of Cuboid is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Cuboid.
Height of Cuboid - (Measured in Meter) - The Height of Cuboid is the vertical distance measured from base to the top of Cuboid.
Width of Cuboid - (Measured in Meter) - The Width of Cuboid is the measure of any one of the pair of parallel edges of base which are smaller than the remaining pair of parallel edges of Cuboid.

STEP 1: Convert Input(s) to Base Unit

Lateral Surface Area of Cuboid: 300 Square Meter --> 300 Square Meter No Conversion Required
Height of Cuboid: 8 Meter --> 8 Meter No Conversion Required
Width of Cuboid: 6 Meter --> 6 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_Space = sqrt((LSA/(2*h)-w)^2+w^2+h^2) --> sqrt((300/(2*8)-6)^2+6^2+8^2)

Evaluating ... ...

d_Space = 16.2037804230988

STEP 3: Convert Result to Output's Unit

16.2037804230988 Meter --> No Conversion Required

FINAL ANSWER

16.2037804230988 ≈ 16.20378 Meter <-- Space Diagonal of Cuboid

(Calculation completed in 00.004 seconds)

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Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< Space Diagonal of Cuboid Calculators

Space Diagonal of Cuboid given Volume, Length, and Height

LaTeX Go Space Diagonal of Cuboid = sqrt(Length of Cuboid^2+(Volume of Cuboid/(Length of Cuboid*Height of Cuboid))^2+Height of Cuboid^2)

Space Diagonal of Cuboid given Volume, Width, and Height

LaTeX Go Space Diagonal of Cuboid = sqrt((Volume of Cuboid/(Width of Cuboid*Height of Cuboid))^2+Width of Cuboid^2+Height of Cuboid^2)

Space Diagonal of Cuboid given Volume, Length, and Width

LaTeX Go Space Diagonal of Cuboid = sqrt(Length of Cuboid^2+Width of Cuboid^2+(Volume of Cuboid/(Length of Cuboid*Width of Cuboid))^2)

Space Diagonal of Cuboid

LaTeX Go Space Diagonal of Cuboid = sqrt(Length of Cuboid^2+Width of Cuboid^2+Height of Cuboid^2)

Space Diagonal of Cuboid given Lateral Surface Area, Width, and Height Formula

LaTeX Go

Space Diagonal of Cuboid = sqrt((Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Width of Cuboid)^2+Width of Cuboid^2+Height of Cuboid^2)
d_Space = sqrt((LSA/(2*h)-w)^2+w^2+h^2)

What is a Cuboid?

In geometry, a Cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube. While mathematical literature refers to any such polyhedron as a cuboid, other sources use "cuboid" to refer to a shape of this type in which each of the faces is a rectangle (and so each pair of adjacent faces meets in a right angle); this more restrictive type of cuboid is also known as a rectangular cuboid, right cuboid, rectangular box, rectangular hexahedron, right rectangular prism, or rectangular parallelepiped.

How to Calculate Space Diagonal of Cuboid given Lateral Surface Area, Width, and Height?

Space Diagonal of Cuboid given Lateral Surface Area, Width, and Height calculator uses Space Diagonal of Cuboid = sqrt((Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Width of Cuboid)^2+Width of Cuboid^2+Height of Cuboid^2) to calculate the Space Diagonal of Cuboid, The Space Diagonal of Cuboid given Lateral Surface Area, Width, and Height formula is defined as the length of the line connecting one vertex to the opposite vertex through the interior of the Cuboid, and is calculated using the lateral surface area, height, and width of the Cuboid. Space Diagonal of Cuboid is denoted by d_Space symbol.

How to calculate Space Diagonal of Cuboid given Lateral Surface Area, Width, and Height using this online calculator? To use this online calculator for Space Diagonal of Cuboid given Lateral Surface Area, Width, and Height, enter Lateral Surface Area of Cuboid (LSA), Height of Cuboid (h) & Width of Cuboid (w) and hit the calculate button. Here is how the Space Diagonal of Cuboid given Lateral Surface Area, Width, and Height calculation can be explained with given input values -> 16.20378 = sqrt((300/(2*8)-6)^2+6^2+8^2).

FAQ

What is Space Diagonal of Cuboid given Lateral Surface Area, Width, and Height?

The Space Diagonal of Cuboid given Lateral Surface Area, Width, and Height formula is defined as the length of the line connecting one vertex to the opposite vertex through the interior of the Cuboid, and is calculated using the lateral surface area, height, and width of the Cuboid and is represented as d_Space = sqrt((LSA/(2*h)-w)^2+w^2+h^2) or Space Diagonal of Cuboid = sqrt((Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Width of Cuboid)^2+Width of Cuboid^2+Height of Cuboid^2). The Lateral Surface Area of Cuboid is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Cuboid, The Height of Cuboid is the vertical distance measured from base to the top of Cuboid & The Width of Cuboid is the measure of any one of the pair of parallel edges of base which are smaller than the remaining pair of parallel edges of Cuboid.

How to calculate Space Diagonal of Cuboid given Lateral Surface Area, Width, and Height?

The Space Diagonal of Cuboid given Lateral Surface Area, Width, and Height formula is defined as the length of the line connecting one vertex to the opposite vertex through the interior of the Cuboid, and is calculated using the lateral surface area, height, and width of the Cuboid is calculated using Space Diagonal of Cuboid = sqrt((Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Width of Cuboid)^2+Width of Cuboid^2+Height of Cuboid^2). To calculate Space Diagonal of Cuboid given Lateral Surface Area, Width, and Height, you need Lateral Surface Area of Cuboid (LSA), Height of Cuboid (h) & Width of Cuboid (w). With our tool, you need to enter the respective value for Lateral Surface Area of Cuboid, Height of Cuboid & Width of Cuboid 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 Space Diagonal of Cuboid?

In this formula, Space Diagonal of Cuboid uses Lateral Surface Area of Cuboid, Height of Cuboid & Width of Cuboid. We can use 3 other way(s) to calculate the same, which is/are as follows -

Space Diagonal of Cuboid = sqrt(Length of Cuboid^2+Width of Cuboid^2+Height of Cuboid^2)
Space Diagonal of Cuboid = sqrt((Volume of Cuboid/(Width of Cuboid*Height of Cuboid))^2+Width of Cuboid^2+Height of Cuboid^2)
Space Diagonal of Cuboid = sqrt(Length of Cuboid^2+(Volume of Cuboid/(Length of Cuboid*Height of Cuboid))^2+Height of Cuboid^2)

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