Base Radius 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%

✖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 given Slant Height [r_Base]

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Formula

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Base Radius of Frustum of Cone given Slant Height

Formula

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

Example

`"5.876894m"="10m"-sqrt(("9m")^2-("8m")^2)`

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Base Radius of Frustum of Cone given Slant Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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

r_Base = r_Top-sqrt(h_Slant^2-h^2) --> 10-sqrt(9^2-8^2)

Evaluating ... ...

r_Base = 5.87689437438234

STEP 3: Convert Result to Output's Unit

5.87689437438234 Meter --> No Conversion Required

FINAL ANSWER

5.87689437438234 ≈ 5.876894 Meter <-- Base Radius of Frustum of Cone

(Calculation completed in 00.004 seconds)

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Credits

Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

Dhruv Walia has created this Calculator and 1100+ more calculators!

Verified by Nikita Kumari

The National Institute of Engineering (NIE), Mysuru

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< 3 Base Radius of Frustum of Cone Calculators

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

Go Base Radius of Frustum of Cone = sqrt(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 given Slant Height

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

Base Radius of Frustum of Cone given Base Area

Go Base Radius of Frustum of Cone = sqrt(Base Area of Frustum of Cone/pi)

< 4 Radius of Frustum of Cone Calculators

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

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

Base Radius of Frustum of Cone given Slant Height

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

Base Radius of Frustum of Cone given Base Area

Go Base Radius of Frustum of Cone = sqrt(Base Area of Frustum of Cone/pi)

Top Radius of Frustum of Cone given Top Area

Go Top Radius of Frustum of Cone = sqrt(Top Area of Frustum of Cone/pi)

Base Radius of Frustum of Cone given Slant Height Formula

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

Base Radius of Frustum of Cone given Slant Height calculator uses Base Radius of Frustum of Cone = Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2) to calculate the Base Radius of Frustum of Cone, The Base Radius of Frustum of Cone given Slant Height formula is defined as the distance between the center and any point on the circumference of the base circular surface of the Frustum of the Cone and calculated using the slant height of the Frustum of Cone. Base Radius of Frustum of Cone is denoted by r_Base symbol.

How to calculate Base Radius of Frustum of Cone given Slant Height using this online calculator? To use this online calculator for Base Radius 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 Radius of Frustum of Cone given Slant Height calculation can be explained with given input values -> 5.876894 = 10-sqrt(9^2-8^2).

FAQ

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

The Base Radius of Frustum of Cone given Slant Height formula is defined as the distance between the center and any point on the circumference of the base circular surface of the Frustum of the Cone and calculated using the slant height of the Frustum of Cone and is represented as r_Base = r_Top-sqrt(h_Slant^2-h^2) or Base Radius of Frustum of Cone = Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^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 Radius of Frustum of Cone given Slant Height?

The Base Radius of Frustum of Cone given Slant Height formula is defined as the distance between the center and any point on the circumference of the base circular surface of the Frustum of the Cone and calculated using the slant height of the Frustum of Cone is calculated using Base Radius of Frustum of Cone = Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2). To calculate Base Radius 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 Radius of Frustum of Cone?

In this formula, Base Radius 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 3 other way(s) to calculate the same, which is/are as follows -

Base Radius of Frustum of Cone = sqrt(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 = sqrt(Base Area of Frustum of Cone/pi)
Base Radius of Frustum of Cone = sqrt(Base Area of Frustum of Cone/pi)

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