Surface to Volume Ratio of Frustum of Cone given Volume and Top Area Calculator

✖Top Area of Frustum of Cone is the total amount of two-dimensional space occupied by the top face of the Frustum of the Cone.ⓘ Top Area of Frustum of Cone [A_Top]			+10% -10%
✖Base Radius of Frustum of Cone is the distance between the center and any point on the circumference of the base circular surface of the Frustum of the Cone.ⓘ Base Radius of Frustum of Cone [r_Base]			+10% -10%
✖Volume of Frustum of Cone is the quantity of three-dimensional space enclosed by the entire surface of the Frustum of the Cone.ⓘ Volume of Frustum of Cone [V]			+10% -10%

✖Surface to Volume Ratio of Frustum of Cone is the numerical ratio of the total surface area of a Frustum of Cone to the volume of the Frustum of Cone.ⓘ Surface to Volume Ratio of Frustum of Cone given Volume and Top Area [R_A/V]

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Surface to Volume Ratio of Frustum of Cone given Volume and Top Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Surface to Volume Ratio of Frustum of Cone = (pi*(((sqrt(Top Area of Frustum of Cone/pi)+Base Radius of Frustum of Cone)*sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Area of Frustum of Cone/pi+Base Radius of Frustum of Cone^2+(sqrt(Top Area of Frustum of Cone/pi)*Base Radius of Frustum of Cone))))^2+(sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2))+Top Area of Frustum of Cone/pi+Base Radius of Frustum of Cone^2))/Volume of Frustum of Cone
R_A/V = (pi*(((sqrt(A_Top/pi)+r_Base)*sqrt(((3*V)/(pi*(A_Top/pi+r_Base^2+(sqrt(A_Top/pi)*r_Base))))^2+(sqrt(A_Top/pi)-r_Base)^2))+A_Top/pi+r_Base^2))/V
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 Frustum of Cone - (Measured in 1 per Meter) - Surface to Volume Ratio of Frustum of Cone is the numerical ratio of the total surface area of a Frustum of Cone to the volume of the Frustum of Cone.
Top Area of Frustum of Cone - (Measured in Square Meter) - Top Area of Frustum of Cone is the total amount of two-dimensional space occupied by the top face of the Frustum of the Cone.
Base Radius of Frustum of Cone - (Measured in Meter) - Base Radius of Frustum of Cone is the distance between the center and any point on the circumference of the base circular surface of the Frustum of the Cone.
Volume of Frustum of Cone - (Measured in Cubic Meter) - Volume of Frustum of Cone is the quantity of three-dimensional space enclosed by the entire surface of the Frustum of the Cone.

STEP 1: Convert Input(s) to Base Unit

Top Area of Frustum of Cone: 315 Square Meter --> 315 Square Meter No Conversion Required
Base Radius of Frustum of Cone: 5 Meter --> 5 Meter No Conversion Required
Volume of Frustum of Cone: 1500 Cubic Meter --> 1500 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = (pi*(((sqrt(A_Top/pi)+r_Base)*sqrt(((3*V)/(pi*(A_Top/pi+r_Base^2+(sqrt(A_Top/pi)*r_Base))))^2+(sqrt(A_Top/pi)-r_Base)^2))+A_Top/pi+r_Base^2))/V --> (pi*(((sqrt(315/pi)+5)*sqrt(((3*1500)/(pi*(315/pi+5^2+(sqrt(315/pi)*5))))^2+(sqrt(315/pi)-5)^2))+315/pi+5^2))/1500

Evaluating ... ...

R_A/V = 0.563753833322765

STEP 3: Convert Result to Output's Unit

0.563753833322765 1 per Meter --> No Conversion Required

FINAL ANSWER

0.563753833322765 ≈ 0.563754 1 per Meter <-- Surface to Volume Ratio of Frustum of Cone

(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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The National Institute of Engineering (NIE), Mysuru

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< Surface to Volume Ratio of Frustum of Cone Calculators

Surface to Volume Ratio of Frustum of Cone given Base Area and Top Area

LaTeX Go Surface to Volume Ratio of Frustum of Cone = (((sqrt(Top Area of Frustum of Cone/pi)+sqrt(Base Area of Frustum of Cone/pi))*sqrt((sqrt(Top Area of Frustum of Cone/pi)-sqrt(Base Area of Frustum of Cone/pi))^2+Height of Frustum of Cone^2))+Top Area of Frustum of Cone/pi+Base Area of Frustum of Cone/pi)/(1/3*Height of Frustum of Cone*(Top Area of Frustum of Cone/pi+Base Area of Frustum of Cone/pi+(sqrt(Top Area of Frustum of Cone/pi)*sqrt(Base Area of Frustum of Cone/pi))))

Surface to Volume Ratio of Frustum of Cone given Base Area

LaTeX Go Surface to Volume Ratio of Frustum of Cone = (((Top Radius of Frustum of Cone+sqrt(Base Area of Frustum of Cone/pi))*sqrt((Top Radius of Frustum of Cone-sqrt(Base Area of Frustum of Cone/pi))^2+Height of Frustum of Cone^2))+Top Radius of Frustum of Cone^2+Base Area of Frustum of Cone)/(1/3*Height of Frustum of Cone*(Top Radius of Frustum of Cone^2+Base Area of Frustum of Cone/pi+(Top Radius of Frustum of Cone*sqrt(Base Area of Frustum of Cone/pi))))

Surface to Volume Ratio of Frustum of Cone given Slant Height

LaTeX Go Surface to Volume Ratio of Frustum of Cone = (((Top Radius of Frustum of Cone+Base Radius of Frustum of Cone)*Slant Height of Frustum of Cone)+Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2)/((sqrt(Slant Height of Frustum of Cone^2-(Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2))/3*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone)))

Surface to Volume Ratio of Frustum of Cone

LaTeX Go Surface to Volume Ratio of Frustum of Cone = (((Top Radius of Frustum of Cone+Base Radius of Frustum of Cone)*sqrt((Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2+Height of Frustum of Cone^2))+Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2)/(1/3*Height of Frustum of Cone*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone)))

Surface to Volume Ratio of Frustum of Cone given Volume and Top Area Formula

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What is a Frustum of Cone?

A Frustum of Cone is the part of cone when it is cut by a (horizontally parallel to the base) plane into two parts. The upper part of the cone remains same in shape but the bottom part makes a frustum.

How to Calculate Surface to Volume Ratio of Frustum of Cone given Volume and Top Area?

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

How to calculate Surface to Volume Ratio of Frustum of Cone given Volume and Top Area using this online calculator? To use this online calculator for Surface to Volume Ratio of Frustum of Cone given Volume and Top Area, enter Top Area of Frustum of Cone (A_Top), Base Radius of Frustum of Cone (r_Base) & Volume of Frustum of Cone (V) and hit the calculate button. Here is how the Surface to Volume Ratio of Frustum of Cone given Volume and Top Area calculation can be explained with given input values -> 0.563754 = (pi*(((sqrt(315/pi)+5)*sqrt(((3*1500)/(pi*(315/pi+5^2+(sqrt(315/pi)*5))))^2+(sqrt(315/pi)-5)^2))+315/pi+5^2))/1500.

FAQ

What is Surface to Volume Ratio of Frustum of Cone given Volume and Top Area?

The Surface to Volume Ratio of Frustum of Cone given Volume and Top Area formula is defined as the numerical ratio of the total surface area of a Frustum of Cone to the volume of the Frustum of Cone, calculated using the volume, top area and base radius of the Frustum of Cone and is represented as R_A/V = (pi*(((sqrt(A_Top/pi)+r_Base)*sqrt(((3*V)/(pi*(A_Top/pi+r_Base^2+(sqrt(A_Top/pi)*r_Base))))^2+(sqrt(A_Top/pi)-r_Base)^2))+A_Top/pi+r_Base^2))/V or Surface to Volume Ratio of Frustum of Cone = (pi*(((sqrt(Top Area of Frustum of Cone/pi)+Base Radius of Frustum of Cone)*sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Area of Frustum of Cone/pi+Base Radius of Frustum of Cone^2+(sqrt(Top Area of Frustum of Cone/pi)*Base Radius of Frustum of Cone))))^2+(sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2))+Top Area of Frustum of Cone/pi+Base Radius of Frustum of Cone^2))/Volume of Frustum of Cone. Top Area of Frustum of Cone is the total amount of two-dimensional space occupied by the top face of the Frustum of the Cone, Base Radius of Frustum of Cone is the distance between the center and any point on the circumference of the base circular surface of the Frustum of the Cone & Volume of Frustum of Cone is the quantity of three-dimensional space enclosed by the entire surface of the Frustum of the Cone.

How to calculate Surface to Volume Ratio of Frustum of Cone given Volume and Top Area?

The Surface to Volume Ratio of Frustum of Cone given Volume and Top Area formula is defined as the numerical ratio of the total surface area of a Frustum of Cone to the volume of the Frustum of Cone, calculated using the volume, top area and base radius of the Frustum of Cone is calculated using Surface to Volume Ratio of Frustum of Cone = (pi*(((sqrt(Top Area of Frustum of Cone/pi)+Base Radius of Frustum of Cone)*sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Area of Frustum of Cone/pi+Base Radius of Frustum of Cone^2+(sqrt(Top Area of Frustum of Cone/pi)*Base Radius of Frustum of Cone))))^2+(sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2))+Top Area of Frustum of Cone/pi+Base Radius of Frustum of Cone^2))/Volume of Frustum of Cone. To calculate Surface to Volume Ratio of Frustum of Cone given Volume and Top Area, you need Top Area of Frustum of Cone (A_Top), Base Radius of Frustum of Cone (r_Base) & Volume of Frustum of Cone (V). With our tool, you need to enter the respective value for Top Area of Frustum of Cone, Base Radius of Frustum of Cone & Volume of Frustum of 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 Frustum of Cone?

In this formula, Surface to Volume Ratio of Frustum of Cone uses Top Area of Frustum of Cone, Base Radius of Frustum of Cone & Volume of Frustum of Cone. We can use 3 other way(s) to calculate the same, which is/are as follows -

Surface to Volume Ratio of Frustum of Cone = (((Top Radius of Frustum of Cone+Base Radius of Frustum of Cone)*sqrt((Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2+Height of Frustum of Cone^2))+Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2)/(1/3*Height of Frustum of Cone*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone)))
Surface to Volume Ratio of Frustum of Cone = (((Top Radius of Frustum of Cone+sqrt(Base Area of Frustum of Cone/pi))*sqrt((Top Radius of Frustum of Cone-sqrt(Base Area of Frustum of Cone/pi))^2+Height of Frustum of Cone^2))+Top Radius of Frustum of Cone^2+Base Area of Frustum of Cone)/(1/3*Height of Frustum of Cone*(Top Radius of Frustum of Cone^2+Base Area of Frustum of Cone/pi+(Top Radius of Frustum of Cone*sqrt(Base Area of Frustum of Cone/pi))))
Surface to Volume Ratio of Frustum of Cone = (((sqrt(Top Area of Frustum of Cone/pi)+sqrt(Base Area of Frustum of Cone/pi))*sqrt((sqrt(Top Area of Frustum of Cone/pi)-sqrt(Base Area of Frustum of Cone/pi))^2+Height of Frustum of Cone^2))+Top Area of Frustum of Cone/pi+Base Area of Frustum of Cone/pi)/(1/3*Height of Frustum of Cone*(Top Area of Frustum of Cone/pi+Base Area of Frustum of Cone/pi+(sqrt(Top Area of Frustum of Cone/pi)*sqrt(Base Area of Frustum of Cone/pi))))

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