Surface to Volume Ratio of Cuboid given Space Diagonal, Height, and Width Solution

STEP 0: Pre-Calculation Summary
Formula Used
Surface to Volume Ratio of Cuboid = (2*((sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Height of Cuboid^2)*Height of Cuboid)+(Height of Cuboid*Width of Cuboid)+(sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Height of Cuboid^2)*Width of Cuboid)))/(sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Height of Cuboid^2)*Width of Cuboid*Height of Cuboid)
RA/V = (2*((sqrt(dSpace^2-w^2-h^2)*h)+(h*w)+(sqrt(dSpace^2-w^2-h^2)*w)))/(sqrt(dSpace^2-w^2-h^2)*w*h)
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
Surface to Volume Ratio of Cuboid - (Measured in 1 per Meter) - The Surface to Volume Ratio of Cuboid is the numerical ratio of the total surface area of a Cuboid to the volume of the Cuboid.
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.
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.
Height of Cuboid - (Measured in Meter) - The Height of Cuboid is the vertical distance measured from base to the top of Cuboid.
STEP 1: Convert Input(s) to Base Unit
Space Diagonal of Cuboid: 16 Meter --> 16 Meter No Conversion Required
Width of Cuboid: 6 Meter --> 6 Meter No Conversion Required
Height of Cuboid: 8 Meter --> 8 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
RA/V = (2*((sqrt(dSpace^2-w^2-h^2)*h)+(h*w)+(sqrt(dSpace^2-w^2-h^2)*w)))/(sqrt(dSpace^2-w^2-h^2)*w*h) --> (2*((sqrt(16^2-6^2-8^2)*8)+(8*6)+(sqrt(16^2-6^2-8^2)*6)))/(sqrt(16^2-6^2-8^2)*6*8)
Evaluating ... ...
RA/V = 0.74346148713842
STEP 3: Convert Result to Output's Unit
0.74346148713842 1 per Meter --> No Conversion Required
FINAL ANSWER
0.74346148713842 0.743461 1 per Meter <-- Surface to Volume Ratio of Cuboid
(Calculation completed in 00.020 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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16 Surface to Volume Ratio of Cuboid Calculators

Surface to Volume Ratio of Cuboid given Space Diagonal, Length, and Height
Go Surface to Volume Ratio of Cuboid = (2*((Length of Cuboid*Height of Cuboid)+(Height of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Height of Cuboid^2))+(Length of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Height of Cuboid^2))))/(Length of Cuboid*Height of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Height of Cuboid^2))
Surface to Volume Ratio of Cuboid given Space Diagonal, Length, and Width
Go Surface to Volume Ratio of Cuboid = (2*((Length of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Width of Cuboid^2))+(sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Width of Cuboid^2)*Width of Cuboid)+(Length of Cuboid*Width of Cuboid)))/(sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Length of Cuboid^2)*Width of Cuboid*Length of Cuboid)
Surface to Volume Ratio of Cuboid given Space Diagonal, Height, and Width
Go Surface to Volume Ratio of Cuboid = (2*((sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Height of Cuboid^2)*Height of Cuboid)+(Height of Cuboid*Width of Cuboid)+(sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Height of Cuboid^2)*Width of Cuboid)))/(sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Height of Cuboid^2)*Width of Cuboid*Height of Cuboid)
Surface to Volume Ratio of Cuboid given Lateral Surface Area, Length, and Height
Go Surface to Volume Ratio of Cuboid = (2*((Length of Cuboid*Height of Cuboid)+(Height of Cuboid*(Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Length of Cuboid))+(Length of Cuboid*(Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Length of Cuboid))))/((Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Length of Cuboid)*Length of Cuboid*Height of Cuboid)
Surface to Volume Ratio of Cuboid given Lateral Surface Area, Height, and Width
Go Surface to Volume Ratio of Cuboid = (2*(((Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Width of Cuboid)*Height of Cuboid)+(Height of Cuboid*Width of Cuboid)+((Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Width of Cuboid)*Width of Cuboid)))/((Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Width of Cuboid)*Width of Cuboid*Height of Cuboid)
Surface to Volume Ratio of Cuboid given Perimeter, Height, and Length
Go Surface to Volume Ratio of Cuboid = (2*((Length of Cuboid*(Perimeter of Cuboid-(4*(Length of Cuboid+Height of Cuboid)))/4)+(Length of Cuboid*Height of Cuboid)+((Perimeter of Cuboid-(4*(Length of Cuboid+Height of Cuboid)))/4*Height of Cuboid)))/(Length of Cuboid*((Perimeter of Cuboid-(4*(Length of Cuboid+Height of Cuboid)))/4)*Height of Cuboid)
Surface to Volume Ratio of Cuboid given Perimeter, Length, and Width
Go Surface to Volume Ratio of Cuboid = (2*((Length of Cuboid*Width of Cuboid)+(Length of Cuboid*(Perimeter of Cuboid-(4*(Length of Cuboid+Width of Cuboid)))/4)+(Width of Cuboid*(Perimeter of Cuboid-(4*(Length of Cuboid+Width of Cuboid)))/4)))/(Length of Cuboid*Width of Cuboid*((Perimeter of Cuboid-(4*(Length of Cuboid+Width of Cuboid)))/4))
Surface to Volume Ratio of Cuboid given Perimeter, Height, and Width
Go Surface to Volume Ratio of Cuboid = (2*(((Perimeter of Cuboid-(4*(Width of Cuboid+Height of Cuboid)))/4*Width of Cuboid)+((Perimeter of Cuboid-(4*(Width of Cuboid+Height of Cuboid)))/4*Height of Cuboid)+(Width of Cuboid*Height of Cuboid)))/((Perimeter of Cuboid-(4*(Width of Cuboid+Height of Cuboid)))/4*Width of Cuboid*Height of Cuboid)
Surface to Volume Ratio of Cuboid
Go Surface to Volume Ratio of Cuboid = (2*((Length of Cuboid*Width of Cuboid)+(Length of Cuboid*Height of Cuboid)+(Width of Cuboid*Height of Cuboid)))/(Length of Cuboid*Width of Cuboid*Height of Cuboid)
Surface to Volume Ratio of Cuboid given Lateral Surface Area, Length, and Width
Go Surface to Volume Ratio of Cuboid = (Lateral Surface Area of Cuboid+(2*Length of Cuboid*Width of Cuboid))/(Length of Cuboid*Width of Cuboid*Lateral Surface Area of Cuboid/(2*(Length of Cuboid+Width of Cuboid)))
Surface to Volume Ratio of Cuboid given Total Surface Area, Length, and Height
Go Surface to Volume Ratio of Cuboid = Total Surface Area of Cuboid/(Length of Cuboid*(Total Surface Area of Cuboid/2-(Height of Cuboid*Length of Cuboid))/(Height of Cuboid+Length of Cuboid)*Height of Cuboid)
Surface to Volume Ratio of Cuboid given Total Surface Area, Length, and Width
Go Surface to Volume Ratio of Cuboid = Total Surface Area of Cuboid/(Length of Cuboid*Width of Cuboid*(Total Surface Area of Cuboid/2-(Length of Cuboid*Width of Cuboid))/(Length of Cuboid+Width of Cuboid))
Surface to Volume Ratio of Cuboid given Total Surface Area, Height, and Width
Go Surface to Volume Ratio of Cuboid = Total Surface Area of Cuboid/((Total Surface Area of Cuboid/2-(Height of Cuboid*Width of Cuboid))/(Height of Cuboid+Width of Cuboid)*Width of Cuboid*Height of Cuboid)
Surface to Volume Ratio of Cuboid given Volume, Length, and Height
Go Surface to Volume Ratio of Cuboid = (2*(Volume of Cuboid/Length of Cuboid+(Height of Cuboid*Length of Cuboid)+Volume of Cuboid/Height of Cuboid))/Volume of Cuboid
Surface to Volume Ratio of Cuboid given Volume, Length, and Width
Go Surface to Volume Ratio of Cuboid = (2*(Volume of Cuboid/Length of Cuboid+(Length of Cuboid*Width of Cuboid)+Volume of Cuboid/Width of Cuboid))/Volume of Cuboid
Surface to Volume Ratio of Cuboid given Volume, Height, and Width
Go Surface to Volume Ratio of Cuboid = (2*(Volume of Cuboid/Width of Cuboid+(Height of Cuboid*Width of Cuboid)+Volume of Cuboid/Height of Cuboid))/Volume of Cuboid

Surface to Volume Ratio of Cuboid given Space Diagonal, Height, and Width Formula

Surface to Volume Ratio of Cuboid = (2*((sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Height of Cuboid^2)*Height of Cuboid)+(Height of Cuboid*Width of Cuboid)+(sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Height of Cuboid^2)*Width of Cuboid)))/(sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Height of Cuboid^2)*Width of Cuboid*Height of Cuboid)
RA/V = (2*((sqrt(dSpace^2-w^2-h^2)*h)+(h*w)+(sqrt(dSpace^2-w^2-h^2)*w)))/(sqrt(dSpace^2-w^2-h^2)*w*h)

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 Surface to Volume Ratio of Cuboid given Space Diagonal, Height, and Width?

Surface to Volume Ratio of Cuboid given Space Diagonal, Height, and Width calculator uses Surface to Volume Ratio of Cuboid = (2*((sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Height of Cuboid^2)*Height of Cuboid)+(Height of Cuboid*Width of Cuboid)+(sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Height of Cuboid^2)*Width of Cuboid)))/(sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Height of Cuboid^2)*Width of Cuboid*Height of Cuboid) to calculate the Surface to Volume Ratio of Cuboid, The Surface to Volume Ratio of Cuboid given Space Diagonal, Height, and Width formula is defined as the numerical ratio of the total surface area of a Cuboid to the volume of the Cuboid, and is calculated using the space diagonal, width, and height of the Cuboid. Surface to Volume Ratio of Cuboid is denoted by RA/V symbol.

How to calculate Surface to Volume Ratio of Cuboid given Space Diagonal, Height, and Width using this online calculator? To use this online calculator for Surface to Volume Ratio of Cuboid given Space Diagonal, Height, and Width, enter Space Diagonal of Cuboid (dSpace), Width of Cuboid (w) & Height of Cuboid (h) and hit the calculate button. Here is how the Surface to Volume Ratio of Cuboid given Space Diagonal, Height, and Width calculation can be explained with given input values -> 0.743461 = (2*((sqrt(16^2-6^2-8^2)*8)+(8*6)+(sqrt(16^2-6^2-8^2)*6)))/(sqrt(16^2-6^2-8^2)*6*8).

FAQ

What is Surface to Volume Ratio of Cuboid given Space Diagonal, Height, and Width?
The Surface to Volume Ratio of Cuboid given Space Diagonal, Height, and Width formula is defined as the numerical ratio of the total surface area of a Cuboid to the volume of the Cuboid, and is calculated using the space diagonal, width, and height of the Cuboid and is represented as RA/V = (2*((sqrt(dSpace^2-w^2-h^2)*h)+(h*w)+(sqrt(dSpace^2-w^2-h^2)*w)))/(sqrt(dSpace^2-w^2-h^2)*w*h) or Surface to Volume Ratio of Cuboid = (2*((sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Height of Cuboid^2)*Height of Cuboid)+(Height of Cuboid*Width of Cuboid)+(sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Height of Cuboid^2)*Width of Cuboid)))/(sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Height of Cuboid^2)*Width of Cuboid*Height of Cuboid). The Space Diagonal of Cuboid is the length of the line connecting one vertex to the opposite vertex through the interior of the 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 & The Height of Cuboid is the vertical distance measured from base to the top of Cuboid.
How to calculate Surface to Volume Ratio of Cuboid given Space Diagonal, Height, and Width?
The Surface to Volume Ratio of Cuboid given Space Diagonal, Height, and Width formula is defined as the numerical ratio of the total surface area of a Cuboid to the volume of the Cuboid, and is calculated using the space diagonal, width, and height of the Cuboid is calculated using Surface to Volume Ratio of Cuboid = (2*((sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Height of Cuboid^2)*Height of Cuboid)+(Height of Cuboid*Width of Cuboid)+(sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Height of Cuboid^2)*Width of Cuboid)))/(sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Height of Cuboid^2)*Width of Cuboid*Height of Cuboid). To calculate Surface to Volume Ratio of Cuboid given Space Diagonal, Height, and Width, you need Space Diagonal of Cuboid (dSpace), Width of Cuboid (w) & Height of Cuboid (h). With our tool, you need to enter the respective value for Space Diagonal of Cuboid, Width of Cuboid & Height 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 Surface to Volume Ratio of Cuboid?
In this formula, Surface to Volume Ratio of Cuboid uses Space Diagonal of Cuboid, Width of Cuboid & Height of Cuboid. We can use 15 other way(s) to calculate the same, which is/are as follows -
  • Surface to Volume Ratio of Cuboid = (2*((Length of Cuboid*Width of Cuboid)+(Length of Cuboid*Height of Cuboid)+(Width of Cuboid*Height of Cuboid)))/(Length of Cuboid*Width of Cuboid*Height of Cuboid)
  • Surface to Volume Ratio of Cuboid = (2*((Length of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Width of Cuboid^2))+(sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Width of Cuboid^2)*Width of Cuboid)+(Length of Cuboid*Width of Cuboid)))/(sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Length of Cuboid^2)*Width of Cuboid*Length of Cuboid)
  • Surface to Volume Ratio of Cuboid = (2*((Length of Cuboid*Height of Cuboid)+(Height of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Height of Cuboid^2))+(Length of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Height of Cuboid^2))))/(Length of Cuboid*Height of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Height of Cuboid^2))
  • Surface to Volume Ratio of Cuboid = (Lateral Surface Area of Cuboid+(2*Length of Cuboid*Width of Cuboid))/(Length of Cuboid*Width of Cuboid*Lateral Surface Area of Cuboid/(2*(Length of Cuboid+Width of Cuboid)))
  • Surface to Volume Ratio of Cuboid = (2*((Length of Cuboid*Height of Cuboid)+(Height of Cuboid*(Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Length of Cuboid))+(Length of Cuboid*(Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Length of Cuboid))))/((Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Length of Cuboid)*Length of Cuboid*Height of Cuboid)
  • Surface to Volume Ratio of Cuboid = (2*(((Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Width of Cuboid)*Height of Cuboid)+(Height of Cuboid*Width of Cuboid)+((Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Width of Cuboid)*Width of Cuboid)))/((Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Width of Cuboid)*Width of Cuboid*Height of Cuboid)
  • Surface to Volume Ratio of Cuboid = Total Surface Area of Cuboid/(Length of Cuboid*Width of Cuboid*(Total Surface Area of Cuboid/2-(Length of Cuboid*Width of Cuboid))/(Length of Cuboid+Width of Cuboid))
  • Surface to Volume Ratio of Cuboid = Total Surface Area of Cuboid/(Length of Cuboid*(Total Surface Area of Cuboid/2-(Height of Cuboid*Length of Cuboid))/(Height of Cuboid+Length of Cuboid)*Height of Cuboid)
  • Surface to Volume Ratio of Cuboid = (2*(Volume of Cuboid/Length of Cuboid+(Length of Cuboid*Width of Cuboid)+Volume of Cuboid/Width of Cuboid))/Volume of Cuboid
  • Surface to Volume Ratio of Cuboid = (2*(Volume of Cuboid/Length of Cuboid+(Height of Cuboid*Length of Cuboid)+Volume of Cuboid/Height of Cuboid))/Volume of Cuboid
  • Surface to Volume Ratio of Cuboid = (2*(Volume of Cuboid/Width of Cuboid+(Height of Cuboid*Width of Cuboid)+Volume of Cuboid/Height of Cuboid))/Volume of Cuboid
  • Surface to Volume Ratio of Cuboid = Total Surface Area of Cuboid/((Total Surface Area of Cuboid/2-(Height of Cuboid*Width of Cuboid))/(Height of Cuboid+Width of Cuboid)*Width of Cuboid*Height of Cuboid)
  • Surface to Volume Ratio of Cuboid = (2*(((Perimeter of Cuboid-(4*(Width of Cuboid+Height of Cuboid)))/4*Width of Cuboid)+((Perimeter of Cuboid-(4*(Width of Cuboid+Height of Cuboid)))/4*Height of Cuboid)+(Width of Cuboid*Height of Cuboid)))/((Perimeter of Cuboid-(4*(Width of Cuboid+Height of Cuboid)))/4*Width of Cuboid*Height of Cuboid)
  • Surface to Volume Ratio of Cuboid = (2*((Length of Cuboid*(Perimeter of Cuboid-(4*(Length of Cuboid+Height of Cuboid)))/4)+(Length of Cuboid*Height of Cuboid)+((Perimeter of Cuboid-(4*(Length of Cuboid+Height of Cuboid)))/4*Height of Cuboid)))/(Length of Cuboid*((Perimeter of Cuboid-(4*(Length of Cuboid+Height of Cuboid)))/4)*Height of Cuboid)
  • Surface to Volume Ratio of Cuboid = (2*((Length of Cuboid*Width of Cuboid)+(Length of Cuboid*(Perimeter of Cuboid-(4*(Length of Cuboid+Width of Cuboid)))/4)+(Width of Cuboid*(Perimeter of Cuboid-(4*(Length of Cuboid+Width of Cuboid)))/4)))/(Length of Cuboid*Width of Cuboid*((Perimeter of Cuboid-(4*(Length of Cuboid+Width of Cuboid)))/4))
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