Height of Truncated Cone given Volume Calculator

✖Volume of Truncated Cone is the total quantity of three dimensional space enclosed by the entire surface of the Truncated Cone.ⓘ Volume of Truncated Cone [V]			+10% -10%
✖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 given Volume [h]

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Formula

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Height of Truncated Cone given Volume

Formula

`"h" = (3*"V")/(pi*("r"_{"Base"}^2+("r"_{"Base"}*"r"_{"Top"})+"r"_{"Top"}^2))`

Example

`"7.100759m"=(3*"290m³")/(pi*(("5m")^2+("5m"*"2m")+("2m")^2))`

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Download Truncated Cone Formulas PDF

Height of Truncated Cone given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Truncated Cone = (3*Volume of Truncated Cone)/(pi*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2))
h = (3*V)/(pi*(r_Base^2+(r_Base*r_Top)+r_Top^2))
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
Volume of Truncated Cone - (Measured in Cubic Meter) - Volume of Truncated Cone is the total quantity of three dimensional space enclosed by the entire surface 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

Volume of Truncated Cone: 290 Cubic Meter --> 290 Cubic 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

h = (3*V)/(pi*(r_Base^2+(r_Base*r_Top)+r_Top^2)) --> (3*290)/(pi*(5^2+(5*2)+2^2))

Evaluating ... ...

h = 7.10075899948456

STEP 3: Convert Result to Output's Unit

7.10075899948456 Meter --> No Conversion Required

FINAL ANSWER

7.10075899948456 ≈ 7.100759 Meter <-- Height of Truncated Cone

(Calculation completed in 00.020 seconds)

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< 4 Height of Truncated Cone Calculators

Height of Truncated Cone given Total Surface Area

Go Height of Truncated Cone = sqrt(((Total Surface Area of Truncated Cone-pi*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2))/(pi*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)))^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2)

Height of Truncated Cone given Curved Surface Area

Go Height of Truncated Cone = 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)

Height of Truncated Cone given Volume

Go Height of Truncated Cone = (3*Volume of Truncated Cone)/(pi*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2))

Height of Truncated Cone given Slant Height

Go Height of Truncated Cone = sqrt(Slant Height of Truncated Cone^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2)

Height of Truncated Cone given Volume 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 Height of Truncated Cone given Volume?

Height of Truncated Cone given Volume calculator uses Height of Truncated Cone = (3*Volume of Truncated Cone)/(pi*(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 Height of Truncated Cone, The Height of Truncated Cone given Volume formula is defined as the vertical distance from the base circular surface to the top most point of the Truncated Cone, and calculated using the volume of Truncated Cone. Height of Truncated Cone is denoted by h symbol.

How to calculate Height of Truncated Cone given Volume using this online calculator? To use this online calculator for Height of Truncated Cone given Volume, enter Volume of Truncated Cone (V), Base Radius of Truncated Cone (r_Base) & Top Radius of Truncated Cone (r_Top) and hit the calculate button. Here is how the Height of Truncated Cone given Volume calculation can be explained with given input values -> 7.100759 = (3*290)/(pi*(5^2+(5*2)+2^2)).

FAQ

What is Height of Truncated Cone given Volume?

The Height of Truncated Cone given Volume formula is defined as the vertical distance from the base circular surface to the top most point of the Truncated Cone, and calculated using the volume of Truncated Cone and is represented as h = (3*V)/(pi*(r_Base^2+(r_Base*r_Top)+r_Top^2)) or Height of Truncated Cone = (3*Volume of Truncated Cone)/(pi*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2)). Volume of Truncated Cone is the total quantity of three dimensional space enclosed by the entire surface 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 Height of Truncated Cone given Volume?

The Height of Truncated Cone given Volume formula is defined as the vertical distance from the base circular surface to the top most point of the Truncated Cone, and calculated using the volume of Truncated Cone is calculated using Height of Truncated Cone = (3*Volume of Truncated Cone)/(pi*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2)). To calculate Height of Truncated Cone given Volume, you need Volume of Truncated Cone (V), Base Radius of Truncated Cone (r_Base) & Top Radius of Truncated Cone (r_Top). With our tool, you need to enter the respective value for Volume 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 Height of Truncated Cone?

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

Height of Truncated Cone = sqrt(Slant Height of Truncated Cone^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2)
Height of Truncated Cone = 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)
Height of Truncated Cone = sqrt(((Total Surface Area of Truncated Cone-pi*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2))/(pi*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)))^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2)

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