Height of Frustum of Cone given Slant Height and Top Area Calculator

✖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%
✖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%

✖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 given Slant Height and Top Area [h]

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Height of Frustum of Cone given Slant Height and Top Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Frustum of Cone = sqrt(Slant Height of Frustum of Cone^2-(sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2)
h = sqrt(h_Slant^2-(sqrt(A_Top/pi)-r_Base)^2)
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

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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Slant Height of Frustum of Cone: 9 Meter --> 9 Meter No Conversion Required
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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = sqrt(h_Slant^2-(sqrt(A_Top/pi)-r_Base)^2) --> sqrt(9^2-(sqrt(315/pi)-5)^2)

Evaluating ... ...

h = 7.474363084837

STEP 3: Convert Result to Output's Unit

7.474363084837 Meter --> No Conversion Required

FINAL ANSWER

7.474363084837 ≈ 7.474363 Meter <-- Height 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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< Height of Frustum of Cone Calculators

Height of Frustum of Cone given Total Surface Area and Base Area

LaTeX Go Height of Frustum of Cone = sqrt(((Total Surface Area of Frustum of Cone/pi-(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)))^2-(Top Radius of Frustum of Cone-sqrt(Base Area of Frustum of Cone/pi))^2)

Height of Frustum of Cone given Volume and Base Area

LaTeX Go Height of Frustum of Cone = (3*Volume of Frustum of Cone)/(pi*(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))))

Height of Frustum of Cone given Volume and Top Area

LaTeX Go Height of Frustum of Cone = (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)))

Height of Frustum of Cone given Volume, Top Area and Base Area

LaTeX Go Height of Frustum of Cone = (3*Volume of Frustum of Cone)/(Top Area of Frustum of Cone+Base Area of Frustum of Cone+(sqrt(Top Area of Frustum of Cone*Base Area of Frustum of Cone)))

Height of Frustum of Cone given Slant Height and Top Area Formula

LaTeX Go

Height of Frustum of Cone = sqrt(Slant Height of Frustum of Cone^2-(sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2)
h = sqrt(h_Slant^2-(sqrt(A_Top/pi)-r_Base)^2)

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 Height of Frustum of Cone given Slant Height and Top Area?

Height of Frustum of Cone given Slant Height and Top Area calculator uses Height of Frustum of Cone = sqrt(Slant Height of Frustum of Cone^2-(sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2) to calculate the Height of Frustum of Cone, The Height of Frustum of Cone given Slant Height and Top Area formula is defined as the maximum vertical distance from the bottom to the top circular face of the Frustum of the Cone and calculated using the slant height, top area, and base radius of the Frustum of Cone. Height of Frustum of Cone is denoted by h symbol.

How to calculate Height of Frustum of Cone given Slant Height and Top Area using this online calculator? To use this online calculator for Height of Frustum of Cone given Slant Height and Top Area, enter Slant Height of Frustum of Cone (h_Slant), Top Area of Frustum of Cone (A_Top) & Base Radius of Frustum of Cone (r_Base) and hit the calculate button. Here is how the Height of Frustum of Cone given Slant Height and Top Area calculation can be explained with given input values -> 7.474363 = sqrt(9^2-(sqrt(315/pi)-5)^2).

FAQ

What is Height of Frustum of Cone given Slant Height and Top Area?

The Height of Frustum of Cone given Slant Height and Top Area formula is defined as the maximum vertical distance from the bottom to the top circular face of the Frustum of the Cone and calculated using the slant height, top area, and base radius of the Frustum of Cone and is represented as h = sqrt(h_Slant^2-(sqrt(A_Top/pi)-r_Base)^2) or Height of Frustum of Cone = sqrt(Slant Height of Frustum of Cone^2-(sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2). 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, 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.

How to calculate Height of Frustum of Cone given Slant Height and Top Area?

The Height of Frustum of Cone given Slant Height and Top Area formula is defined as the maximum vertical distance from the bottom to the top circular face of the Frustum of the Cone and calculated using the slant height, top area, and base radius of the Frustum of Cone is calculated using Height of Frustum of Cone = sqrt(Slant Height of Frustum of Cone^2-(sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2). To calculate Height of Frustum of Cone given Slant Height and Top Area, you need Slant Height of Frustum of Cone (h_Slant), Top Area of Frustum of Cone (A_Top) & Base Radius of Frustum of Cone (r_Base). With our tool, you need to enter the respective value for Slant Height of Frustum of Cone, Top Area of Frustum of Cone & Base Radius 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 Height of Frustum of Cone?

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

Height of Frustum of Cone = (3*Volume of Frustum of Cone)/(pi*(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))))
Height of Frustum of Cone = (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)))
Height of Frustum of Cone = (3*Volume of Frustum of Cone)/(Top Area of Frustum of Cone+Base Area of Frustum of Cone+(sqrt(Top Area of Frustum of Cone*Base Area of Frustum of Cone)))

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