Surface to Volume Ratio of Truncated Cone Calculator

✖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.ⓘ Base Radius of Truncated Cone [r_Base]			+10% -10%
✖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.ⓘ Top Radius of Truncated Cone [r_Top]			+10% -10%
✖Height of Truncated Cone is the vertical distance from the base circular surface to the top most point of the Truncated Cone.ⓘ Height of Truncated Cone [h]			+10% -10%

✖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.ⓘ Surface to Volume Ratio of Truncated Cone [R_A/V]

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Formula

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Surface to Volume Ratio of Truncated Cone

Formula

`"R"_{"A/V"} = 3*("r"_{"Base"}^2+"r"_{"Top"}^2+(sqrt(("r"_{"Top"}-"r"_{"Base"})^2+"h"^2)*("r"_{"Base"}+"r"_{"Top"})))/("h"*("r"_{"Base"}^2+("r"_{"Base"}*"r"_{"Top"})+"r"_{"Top"}^2))`

Example

`"0.90451m⁻¹"=3*(("5m")^2+("2m")^2+(sqrt(("2m"-"5m")^2+("7m")^2)*("5m"+"2m")))/("7m"*(("5m")^2+("5m"*"2m")+("2m")^2))`

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Surface to Volume Ratio of Truncated Cone Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
R_A/V = 3*(r_Base^2+r_Top^2+(sqrt((r_Top-r_Base)^2+h^2)*(r_Base+r_Top)))/(h*(r_Base^2+(r_Base*r_Top)+r_Top^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

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.
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.
Height of Truncated Cone - (Measured in Meter) - Height of Truncated Cone is the vertical distance from the base circular surface to the top most point of the Truncated Cone.

STEP 1: Convert Input(s) to Base Unit

Base Radius of Truncated Cone: 5 Meter --> 5 Meter No Conversion Required
Top Radius of Truncated Cone: 2 Meter --> 2 Meter No Conversion Required
Height of Truncated Cone: 7 Meter --> 7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = 3*(r_Base^2+r_Top^2+(sqrt((r_Top-r_Base)^2+h^2)*(r_Base+r_Top)))/(h*(r_Base^2+(r_Base*r_Top)+r_Top^2)) --> 3*(5^2+2^2+(sqrt((2-5)^2+7^2)*(5+2)))/(7*(5^2+(5*2)+2^2))

Evaluating ... ...

R_A/V = 0.904510019132389

STEP 3: Convert Result to Output's Unit

0.904510019132389 1 per Meter --> No Conversion Required

FINAL ANSWER

0.904510019132389 ≈ 0.90451 1 per Meter <-- Surface to Volume Ratio of Truncated Cone

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 3D Geometry » Cone » Truncated Cone » Surface to Volume Ratio of Truncated Cone » Surface to Volume Ratio of Truncated Cone

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Created by Nikhil

Mumbai University (DJSCE), Mumbai

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Verified by Dhruv Walia

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

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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 Formula

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?

Surface to Volume Ratio of Truncated Cone calculator uses 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)) to calculate the Surface to Volume Ratio of Truncated Cone, The Surface to Volume Ratio of Truncated Cone formula is defined as the numerical ratio of the total surface area of Truncated Cone to the volume of Truncated Cone. Surface to Volume Ratio of Truncated Cone is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Truncated Cone using this online calculator? To use this online calculator for Surface to Volume Ratio of Truncated Cone, enter Base Radius of Truncated Cone (r_Base), Top Radius of Truncated Cone (r_Top) & Height of Truncated Cone (h) and hit the calculate button. Here is how the Surface to Volume Ratio of Truncated Cone calculation can be explained with given input values -> 0.90451 = 3*(5^2+2^2+(sqrt((2-5)^2+7^2)*(5+2)))/(7*(5^2+(5*2)+2^2)).

FAQ

What is Surface to Volume Ratio of Truncated Cone?

The Surface to Volume Ratio of Truncated Cone formula is defined as the numerical ratio of the total surface area of Truncated Cone to the volume of Truncated Cone and is represented as R_A/V = 3*(r_Base^2+r_Top^2+(sqrt((r_Top-r_Base)^2+h^2)*(r_Base+r_Top)))/(h*(r_Base^2+(r_Base*r_Top)+r_Top^2)) or 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)). 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 & Height of Truncated Cone is the vertical distance from the base circular surface to the top most point of the Truncated Cone.

How to calculate Surface to Volume Ratio of Truncated Cone?

The Surface to Volume Ratio of Truncated Cone formula is defined as the numerical ratio of the total surface area of Truncated Cone to the volume of Truncated Cone is calculated using 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)). To calculate Surface to Volume Ratio of Truncated Cone, you need Base Radius of Truncated Cone (r_Base), Top Radius of Truncated Cone (r_Top) & Height of Truncated Cone (h). With our tool, you need to enter the respective value for Base Radius of Truncated Cone, Top Radius of Truncated Cone & Height 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 Base Radius of Truncated Cone, Top Radius of Truncated Cone & Height 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 = (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 = (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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