Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Top Radius Calculator

✖Top Radius of Frustum of Cone is the distance between the center and any point on the circumference of the top circular surface of the Frustum of the Cone.ⓘ Top Radius of Frustum of Cone [r_Top]			+10% -10%
✖The Slant Height of Frustum of Cone is the length of the line segment joining the extremities of two parallel radii, drawn in the same direction of the two circular bases.ⓘ Slant Height of Frustum of Cone [h_Slant]			+10% -10%
✖Height of Frustum of Cone is the maximum vertical distance from the bottom to the top circular face of the Frustum of the Cone.ⓘ Height of Frustum of Cone [h]			+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 Slant Height, Height and Top Radius [R_A/V]

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Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Top Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Surface to Volume Ratio of Frustum of Cone = (((2*Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))*Slant Height of Frustum of Cone)+Top Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2)/(1/3*Height of Frustum of Cone*(Top Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2+(Top Radius of Frustum of Cone*(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)))))
R_A/V = (((2*r_Top-sqrt(h_Slant^2-h^2))*h_Slant)+r_Top^2+(r_Top-sqrt(h_Slant^2-h^2))^2)/(1/3*h*(r_Top^2+(r_Top-sqrt(h_Slant^2-h^2))^2+(r_Top*(r_Top-sqrt(h_Slant^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

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 Radius of Frustum of Cone - (Measured in Meter) - Top Radius of Frustum of Cone is the distance between the center and any point on the circumference of the top circular surface of the Frustum of the Cone.
Slant Height of Frustum of Cone - (Measured in Meter) - The Slant Height of Frustum of Cone is the length of the line segment joining the extremities of two parallel radii, drawn in the same direction of the two circular bases.
Height of Frustum of Cone - (Measured in Meter) - Height of Frustum of Cone is the maximum vertical distance from the bottom to the top circular face of the Frustum of the Cone.

STEP 1: Convert Input(s) to Base Unit

Top Radius of Frustum of Cone: 10 Meter --> 10 Meter No Conversion Required
Slant Height of Frustum of Cone: 9 Meter --> 9 Meter No Conversion Required
Height of Frustum of Cone: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = (((2*r_Top-sqrt(h_Slant^2-h^2))*h_Slant)+r_Top^2+(r_Top-sqrt(h_Slant^2-h^2))^2)/(1/3*h*(r_Top^2+(r_Top-sqrt(h_Slant^2-h^2))^2+(r_Top*(r_Top-sqrt(h_Slant^2-h^2))))) --> (((2*10-sqrt(9^2-8^2))*9)+10^2+(10-sqrt(9^2-8^2))^2)/(1/3*8*(10^2+(10-sqrt(9^2-8^2))^2+(10*(10-sqrt(9^2-8^2)))))

Evaluating ... ...

R_A/V = 0.538192187304713

STEP 3: Convert Result to Output's Unit

0.538192187304713 1 per Meter --> No Conversion Required

FINAL ANSWER

0.538192187304713 ≈ 0.538192 1 per Meter <-- Surface to Volume Ratio of Frustum of Cone

(Calculation completed in 00.020 seconds)

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Home » Math » Geometry » 3D Geometry » Frustum of Cone » Surface to Volume Ratio of Frustum of Cone » Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Top Radius

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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 Slant Height, Height and Top Radius 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 Slant Height, Height and Top Radius?

Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Top Radius calculator uses Surface to Volume Ratio of Frustum of Cone = (((2*Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))*Slant Height of Frustum of Cone)+Top Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2)/(1/3*Height of Frustum of Cone*(Top Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2+(Top Radius of Frustum of Cone*(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))))) to calculate the Surface to Volume Ratio of Frustum of Cone, The Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Top Radius 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 slant height, top radius and height 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 Slant Height, Height and Top Radius using this online calculator? To use this online calculator for Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Top Radius, enter Top Radius of Frustum of Cone (r_Top), Slant Height of Frustum of Cone (h_Slant) & Height of Frustum of Cone (h) and hit the calculate button. Here is how the Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Top Radius calculation can be explained with given input values -> 0.538192 = (((2*10-sqrt(9^2-8^2))*9)+10^2+(10-sqrt(9^2-8^2))^2)/(1/3*8*(10^2+(10-sqrt(9^2-8^2))^2+(10*(10-sqrt(9^2-8^2))))).

FAQ

What is Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Top Radius?

The Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Top Radius 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 slant height, top radius and height of the Frustum of Cone and is represented as R_A/V = (((2*r_Top-sqrt(h_Slant^2-h^2))*h_Slant)+r_Top^2+(r_Top-sqrt(h_Slant^2-h^2))^2)/(1/3*h*(r_Top^2+(r_Top-sqrt(h_Slant^2-h^2))^2+(r_Top*(r_Top-sqrt(h_Slant^2-h^2))))) or Surface to Volume Ratio of Frustum of Cone = (((2*Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))*Slant Height of Frustum of Cone)+Top Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2)/(1/3*Height of Frustum of Cone*(Top Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2+(Top Radius of Frustum of Cone*(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))))). Top Radius of Frustum of Cone is the distance between the center and any point on the circumference of the top circular surface of the Frustum of the Cone, The Slant Height of Frustum of Cone is the length of the line segment joining the extremities of two parallel radii, drawn in the same direction of the two circular bases & Height of Frustum of Cone is the maximum vertical distance from the bottom to the top circular face of the Frustum of the Cone.

How to calculate Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Top Radius?

The Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Top Radius 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 slant height, top radius and height of the Frustum of Cone is calculated using Surface to Volume Ratio of Frustum of Cone = (((2*Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))*Slant Height of Frustum of Cone)+Top Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2)/(1/3*Height of Frustum of Cone*(Top Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2+(Top Radius of Frustum of Cone*(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))))). To calculate Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Top Radius, you need Top Radius of Frustum of Cone (r_Top), Slant Height of Frustum of Cone (h_Slant) & Height of Frustum of Cone (h). With our tool, you need to enter the respective value for Top Radius of Frustum of Cone, Slant Height of Frustum of Cone & Height 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 Radius of Frustum of Cone, Slant Height of Frustum of Cone & Height 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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