Base Area of Frustum of Cone given Slant Height 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%

✖The Base Area of Frustum of Cone is the total amount of two-dimensional space occupied by the base face of the Frustum of the Cone.ⓘ Base Area of Frustum of Cone given Slant Height [A_Base]

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Formula

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Base Area of Frustum of Cone given Slant Height

Formula

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

Example

`"108.504m²"=pi*("10m"-sqrt(("9m")^2-("8m")^2))^2`

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Base Area of Frustum of Cone given Slant Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Base Area of Frustum of Cone = pi*(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2
A_Base = pi*(r_Top-sqrt(h_Slant^2-h^2))^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

Base Area of Frustum of Cone - (Measured in Square Meter) - The Base Area of Frustum of Cone is the total amount of two-dimensional space occupied by the base face of the Frustum of the 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

A_Base = pi*(r_Top-sqrt(h_Slant^2-h^2))^2 --> pi*(10-sqrt(9^2-8^2))^2

Evaluating ... ...

A_Base = 108.503973601702

STEP 3: Convert Result to Output's Unit

108.503973601702 Square Meter --> No Conversion Required

FINAL ANSWER

108.503973601702 ≈ 108.504 Square Meter <-- Base Area 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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The National Institute of Engineering (NIE), Mysuru

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< 3 Base Area of Frustum of Cone Calculators

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

Go Base Area of Frustum of Cone = pi*(sqrt(Top Area of Frustum of Cone/pi)-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2

Base Area of Frustum of Cone given Slant Height

Go Base Area of Frustum of Cone = pi*(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2

Base Area of Frustum of Cone

Go Base Area of Frustum of Cone = pi*Base Radius of Frustum of Cone^2

Base Area of Frustum of Cone given Slant Height Formula

Base Area of Frustum of Cone = pi*(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2
A_Base = pi*(r_Top-sqrt(h_Slant^2-h^2))^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 Base Area of Frustum of Cone given Slant Height?

Base Area of Frustum of Cone given Slant Height calculator uses Base Area of Frustum of Cone = pi*(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2 to calculate the Base Area of Frustum of Cone, The Base Area of Frustum of Cone given Slant Height formula is defined as the total amount of two-dimensional space occupied by the base face of the Frustum of the Cone and calculated using the slant height of the Frustum of Cone. Base Area of Frustum of Cone is denoted by A_Base symbol.

How to calculate Base Area of Frustum of Cone given Slant Height using this online calculator? To use this online calculator for Base Area of Frustum of Cone given Slant Height, 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 Base Area of Frustum of Cone given Slant Height calculation can be explained with given input values -> 108.504 = pi*(10-sqrt(9^2-8^2))^2.

FAQ

What is Base Area of Frustum of Cone given Slant Height?

The Base Area of Frustum of Cone given Slant Height formula is defined as the total amount of two-dimensional space occupied by the base face of the Frustum of the Cone and calculated using the slant height of the Frustum of Cone and is represented as A_Base = pi*(r_Top-sqrt(h_Slant^2-h^2))^2 or Base Area of Frustum of Cone = pi*(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 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 Base Area of Frustum of Cone given Slant Height?

The Base Area of Frustum of Cone given Slant Height formula is defined as the total amount of two-dimensional space occupied by the base face of the Frustum of the Cone and calculated using the slant height of the Frustum of Cone is calculated using Base Area of Frustum of Cone = pi*(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2. To calculate Base Area of Frustum of Cone given Slant Height, 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 Base Area of Frustum of Cone?

In this formula, Base Area 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 2 other way(s) to calculate the same, which is/are as follows -

Base Area of Frustum of Cone = pi*(sqrt(Top Area of Frustum of Cone/pi)-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2
Base Area of Frustum of Cone = pi*Base Radius of Frustum of Cone^2

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