Surface to Volume Ratio of Truncated Cone given Curved Surface Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
Surface to Volume Ratio of Truncated Cone = (Curved Surface Area of Truncated Cone+pi*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2))/((pi*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2))/3*sqrt((Curved Surface Area of Truncated Cone/(pi*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)))^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2))
RA/V = (CSA+pi*(rBase^2+rTop^2))/((pi*(rBase^2+(rBase*rTop)+rTop^2))/3*sqrt((CSA/(pi*(rBase+rTop)))^2-(rBase-rTop)^2))
This formula uses 1 Constants, 1 Functions, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
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 Truncated Cone - (Measured in 1 per Meter) - The Surface to Volume Ratio of Truncated Cone is the numerical ratio of the total surface area of Truncated Cone to the volume of Truncated Cone.
Curved Surface Area of Truncated Cone - (Measured in Square Meter) - Curved Surface Area of Truncated Cone is the quantity of plane enclosed on curved surfaces (that is, top and bottom faces are excluded) of the Truncated Cone.
Base Radius of Truncated Cone - (Measured in Meter) - Base Radius of Truncated Cone is the distance between the center and any point on the circumference of the base circular surface of the Truncated Cone.
Top Radius of Truncated Cone - (Measured in Meter) - Top Radius of Truncated Cone is the distance between the center and any point on the circumference of the top circular surface of the Truncated Cone.
STEP 1: Convert Input(s) to Base Unit
Curved Surface Area of Truncated Cone: 170 Square Meter --> 170 Square Meter No Conversion Required
Base Radius of Truncated Cone: 5 Meter --> 5 Meter No Conversion Required
Top Radius of Truncated Cone: 2 Meter --> 2 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
RA/V = (CSA+pi*(rBase^2+rTop^2))/((pi*(rBase^2+(rBase*rTop)+rTop^2))/3*sqrt((CSA/(pi*(rBase+rTop)))^2-(rBase-rTop)^2)) --> (170+pi*(5^2+2^2))/((pi*(5^2+(5*2)+2^2))/3*sqrt((170/(pi*(5+2)))^2-(5-2)^2))
Evaluating ... ...
RA/V = 0.897363036708529
STEP 3: Convert Result to Output's Unit
0.897363036708529 1 per Meter --> No Conversion Required
FINAL ANSWER
0.897363036708529 0.897363 1 per Meter <-- Surface to Volume Ratio of Truncated Cone
(Calculation completed in 00.020 seconds)

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Mumbai University (DJSCE), Mumbai
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3 Surface to Volume Ratio of Truncated Cone Calculators

Surface to Volume Ratio of Truncated Cone given Curved Surface Area
Go Surface to Volume Ratio of Truncated Cone = (Curved Surface Area of Truncated Cone+pi*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2))/((pi*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2))/3*sqrt((Curved Surface Area of Truncated Cone/(pi*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)))^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2))
Surface to Volume Ratio of Truncated Cone given Slant Height
Go Surface to Volume Ratio of Truncated Cone = (3*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2+(Slant Height of Truncated Cone*(Base Radius of Truncated Cone+Top Radius of Truncated Cone))))/(sqrt(Slant Height of Truncated Cone^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2)*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2))
Surface to Volume Ratio of Truncated Cone
Go Surface to Volume Ratio of Truncated Cone = 3*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2+(sqrt((Top Radius of Truncated Cone-Base Radius of Truncated Cone)^2+Height of Truncated Cone^2)*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)))/(Height of Truncated Cone*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2))

Surface to Volume Ratio of Truncated Cone given Curved Surface Area Formula

Surface to Volume Ratio of Truncated Cone = (Curved Surface Area of Truncated Cone+pi*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2))/((pi*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2))/3*sqrt((Curved Surface Area of Truncated Cone/(pi*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)))^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2))
RA/V = (CSA+pi*(rBase^2+rTop^2))/((pi*(rBase^2+(rBase*rTop)+rTop^2))/3*sqrt((CSA/(pi*(rBase+rTop)))^2-(rBase-rTop)^2))

What is a Truncated Cone?

A Truncated Cone is basically a circular cone of which top is cut or 'truncated' by a horizontal plane. Or in another way, a Truncated Cone is formed when a smaller circular cone is cut from the top of a larger circular cone. The Truncated has two circular surfaces - one on top and another on the bottom, and a lateral curved surface. The slant height is the shortest distance between the two circles on the lateral surface, which is the surface without the circles.

How to Calculate Surface to Volume Ratio of Truncated Cone given Curved Surface Area?

Surface to Volume Ratio of Truncated Cone given Curved Surface Area calculator uses Surface to Volume Ratio of Truncated Cone = (Curved Surface Area of Truncated Cone+pi*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2))/((pi*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2))/3*sqrt((Curved Surface Area of Truncated Cone/(pi*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)))^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2)) to calculate the Surface to Volume Ratio of Truncated Cone, The Surface to Volume Ratio of Truncated Cone given Curved Surface Area formula is defined as the numerical ratio of the total surface area of Truncated Cone to the volume of Truncated Cone, and calculated using the curved surface area of Truncated Cone. Surface to Volume Ratio of Truncated Cone is denoted by RA/V symbol.

How to calculate Surface to Volume Ratio of Truncated Cone given Curved Surface Area using this online calculator? To use this online calculator for Surface to Volume Ratio of Truncated Cone given Curved Surface Area, enter Curved Surface Area of Truncated Cone (CSA), Base Radius of Truncated Cone (rBase) & Top Radius of Truncated Cone (rTop) and hit the calculate button. Here is how the Surface to Volume Ratio of Truncated Cone given Curved Surface Area calculation can be explained with given input values -> 0.897363 = (170+pi*(5^2+2^2))/((pi*(5^2+(5*2)+2^2))/3*sqrt((170/(pi*(5+2)))^2-(5-2)^2)).

FAQ

What is Surface to Volume Ratio of Truncated Cone given Curved Surface Area?
The Surface to Volume Ratio of Truncated Cone given Curved Surface Area formula is defined as the numerical ratio of the total surface area of Truncated Cone to the volume of Truncated Cone, and calculated using the curved surface area of Truncated Cone and is represented as RA/V = (CSA+pi*(rBase^2+rTop^2))/((pi*(rBase^2+(rBase*rTop)+rTop^2))/3*sqrt((CSA/(pi*(rBase+rTop)))^2-(rBase-rTop)^2)) or Surface to Volume Ratio of Truncated Cone = (Curved Surface Area of Truncated Cone+pi*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2))/((pi*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2))/3*sqrt((Curved Surface Area of Truncated Cone/(pi*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)))^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2)). Curved Surface Area of Truncated Cone is the quantity of plane enclosed on curved surfaces (that is, top and bottom faces are excluded) of the Truncated Cone, Base Radius of Truncated Cone is the distance between the center and any point on the circumference of the base circular surface of the Truncated Cone & Top Radius of Truncated Cone is the distance between the center and any point on the circumference of the top circular surface of the Truncated Cone.
How to calculate Surface to Volume Ratio of Truncated Cone given Curved Surface Area?
The Surface to Volume Ratio of Truncated Cone given Curved Surface Area formula is defined as the numerical ratio of the total surface area of Truncated Cone to the volume of Truncated Cone, and calculated using the curved surface area of Truncated Cone is calculated using Surface to Volume Ratio of Truncated Cone = (Curved Surface Area of Truncated Cone+pi*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2))/((pi*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2))/3*sqrt((Curved Surface Area of Truncated Cone/(pi*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)))^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2)). To calculate Surface to Volume Ratio of Truncated Cone given Curved Surface Area, you need Curved Surface Area of Truncated Cone (CSA), Base Radius of Truncated Cone (rBase) & Top Radius of Truncated Cone (rTop). With our tool, you need to enter the respective value for Curved Surface Area of Truncated Cone, Base Radius of Truncated Cone & Top Radius of Truncated Cone 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 Truncated Cone?
In this formula, Surface to Volume Ratio of Truncated Cone uses Curved Surface Area of Truncated Cone, Base Radius of Truncated Cone & Top Radius of Truncated Cone. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Surface to Volume Ratio of Truncated Cone = 3*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2+(sqrt((Top Radius of Truncated Cone-Base Radius of Truncated Cone)^2+Height of Truncated Cone^2)*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)))/(Height of Truncated Cone*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2))
  • Surface to Volume Ratio of Truncated Cone = (3*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2+(Slant Height of Truncated Cone*(Base Radius of Truncated Cone+Top Radius of Truncated Cone))))/(sqrt(Slant Height of Truncated Cone^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2)*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2))
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