Top Area of Frustum of Cone given Slant Height 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%
✖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%
✖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%

✖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 given Slant Height [A_Top]

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Formula

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Top Area of Frustum of Cone given Slant Height

Formula

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

Example

`"261.4781m²"=pi*(sqrt(("9m")^2-("8m")^2)+"5m")^2`

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Top Area of Frustum of Cone given Slant Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.
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
Height of Frustum of Cone: 8 Meter --> 8 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

A_Top = pi*(sqrt(h_Slant^2-h^2)+r_Base)^2 --> pi*(sqrt(9^2-8^2)+5)^2

Evaluating ... ...

A_Top = 261.478074884923

STEP 3: Convert Result to Output's Unit

261.478074884923 Square Meter --> No Conversion Required

FINAL ANSWER

261.478074884923 ≈ 261.4781 Square Meter <-- Top Area of Frustum of Cone

(Calculation completed in 00.008 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 Top Area of Frustum of Cone Calculators

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

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

Top Area of Frustum of Cone given Slant Height

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

Top Area of Frustum of Cone

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

Top Area of Frustum of Cone given Slant Height Formula

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

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

How to calculate Top Area of Frustum of Cone given Slant Height using this online calculator? To use this online calculator for Top Area of Frustum of Cone given Slant Height, enter Slant Height of Frustum of Cone (h_Slant), Height of Frustum of Cone (h) & Base Radius of Frustum of Cone (r_Base) and hit the calculate button. Here is how the Top Area of Frustum of Cone given Slant Height calculation can be explained with given input values -> 261.4781 = pi*(sqrt(9^2-8^2)+5)^2.

FAQ

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

The Top Area of Frustum of Cone given Slant Height formula is defined as the total amount of two-dimensional space occupied by the top face of the Frustum of the Cone and calculated using the slant height of the Frustum of Cone and is represented as A_Top = pi*(sqrt(h_Slant^2-h^2)+r_Base)^2 or Top Area of Frustum of Cone = pi*(sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+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, Height of Frustum of Cone is the maximum vertical distance from the bottom to the top circular 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 Top Area of Frustum of Cone given Slant Height?

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

In this formula, Top Area of Frustum of Cone uses Slant Height of Frustum of Cone, Height of Frustum of Cone & Base Radius of Frustum of Cone. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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