Height of Truncated Cone given Slant Height Calculator

✖Slant Height of Truncated Cone is the length of the straight line connecting any point on the base to the truncated top circular face of the Truncated Cone.ⓘ Slant Height of Truncated Cone [h_Slant]			+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 Slant Height [h]

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Formula

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Height of Truncated Cone given Slant Height

Formula

`"h" = sqrt("h"_{"Slant"}^2-("r"_{"Base"}-"r"_{"Top"})^2)`

Example

`"7.416198m"=sqrt(("8m")^2-("5m"-"2m")^2)`

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Height of Truncated Cone given Slant Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Truncated Cone = sqrt(Slant Height of Truncated Cone^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2)
h = sqrt(h_Slant^2-(r_Base-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

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.
Slant Height of Truncated Cone - (Measured in Meter) - Slant Height of Truncated Cone is the length of the straight line connecting any point on the base to the truncated top circular face 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

Slant Height of Truncated Cone: 8 Meter --> 8 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 = sqrt(h_Slant^2-(r_Base-r_Top)^2) --> sqrt(8^2-(5-2)^2)

Evaluating ... ...

h = 7.41619848709566

STEP 3: Convert Result to Output's Unit

7.41619848709566 Meter --> No Conversion Required

FINAL ANSWER

7.41619848709566 ≈ 7.416198 Meter <-- Height of Truncated Cone

(Calculation completed in 00.022 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 Slant Height Formula

Height of Truncated Cone = sqrt(Slant Height of Truncated Cone^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2)
h = sqrt(h_Slant^2-(r_Base-r_Top)^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 Height of Truncated Cone given Slant Height?

Height of Truncated Cone given Slant Height calculator uses Height of Truncated Cone = sqrt(Slant Height of Truncated Cone^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2) to calculate the Height of Truncated Cone, The Height of Truncated Cone given Slant Height 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 slant height of Truncated Cone. Height of Truncated Cone is denoted by h symbol.

How to calculate Height of Truncated Cone given Slant Height using this online calculator? To use this online calculator for Height of Truncated Cone given Slant Height, enter Slant Height of Truncated Cone (h_Slant), 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 Slant Height calculation can be explained with given input values -> 7.416198 = sqrt(8^2-(5-2)^2).

FAQ

What is Height of Truncated Cone given Slant Height?

The Height of Truncated Cone given Slant Height 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 slant height of Truncated Cone and is represented as h = sqrt(h_Slant^2-(r_Base-r_Top)^2) or Height of Truncated Cone = sqrt(Slant Height of Truncated Cone^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2). Slant Height of Truncated Cone is the length of the straight line connecting any point on the base to the truncated top circular face 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 Slant Height?

The Height of Truncated Cone given Slant Height 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 slant height of Truncated Cone is calculated using Height of Truncated Cone = sqrt(Slant Height of Truncated Cone^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2). To calculate Height of Truncated Cone given Slant Height, you need Slant Height of Truncated Cone (h_Slant), 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 Slant Height 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 Slant Height 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 = (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 = 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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