Curved Surface Area of Frustum of Cone given Volume 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%
✖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%
✖Volume of Frustum of Cone is the quantity of three-dimensional space enclosed by the entire surface of the Frustum of the Cone.ⓘ Volume of Frustum of Cone [V]			+10% -10%

✖Curved Surface Area of Frustum of Cone is the quantity of plane enclosed by curved surfaces (that is, top and bottom faces are excluded) of the Frustum of the Cone.ⓘ Curved Surface Area of Frustum of Cone given Volume [CSA]

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Curved Surface Area of Frustum of Cone given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Curved Surface Area of Frustum of Cone = pi*(Top Radius of Frustum of Cone+Base Radius of Frustum of Cone)*sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone))))^2+(Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2)
CSA = pi*(r_Top+r_Base)*sqrt(((3*V)/(pi*(r_Top^2+r_Base^2+(r_Top*r_Base))))^2+(r_Top-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

Curved Surface Area of Frustum of Cone - (Measured in Square Meter) - Curved Surface Area of Frustum of Cone is the quantity of plane enclosed by curved surfaces (that is, top and bottom faces are excluded) 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.
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.
Volume of Frustum of Cone - (Measured in Cubic Meter) - Volume of Frustum of Cone is the quantity of three-dimensional space enclosed by the entire surface 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
Base Radius of Frustum of Cone: 5 Meter --> 5 Meter No Conversion Required
Volume of Frustum of Cone: 1500 Cubic Meter --> 1500 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

CSA = pi*(r_Top+r_Base)*sqrt(((3*V)/(pi*(r_Top^2+r_Base^2+(r_Top*r_Base))))^2+(r_Top-r_Base)^2) --> pi*(10+5)*sqrt(((3*1500)/(pi*(10^2+5^2+(10*5))))^2+(10-5)^2)

Evaluating ... ...

CSA = 451.986764142723

STEP 3: Convert Result to Output's Unit

451.986764142723 Square Meter --> No Conversion Required

FINAL ANSWER

451.986764142723 ≈ 451.9868 Square Meter <-- Curved Surface 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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< Curved Surface Area of Frustum of Cone Calculators

Curved Surface Area of Frustum of Cone given Slant Height, Height and Base Area

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

Curved Surface Area of Frustum of Cone given Slant Height, Base Area and Top Area

LaTeX Go Curved Surface Area of Frustum of Cone = pi*(sqrt(Top Area of Frustum of Cone/pi)+sqrt(Base Area of Frustum of Cone/pi))*Slant Height of Frustum of Cone

Curved Surface Area of Frustum of Cone given Slant Height, Height and Base Radius

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

Curved Surface Area of Frustum of Cone given Slant Height, Height and Top Radius

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

< Surface Area of Frustum of Cone Calculators

Total Surface Area of Frustum of Cone

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

Total Surface Area of Frustum of Cone given Slant Height

LaTeX Go Total Surface Area of Frustum of Cone = pi*(((Top Radius of Frustum of Cone+Base Radius of Frustum of Cone)*Slant Height of Frustum of Cone)+Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2)

Base Area of Frustum of Cone

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

Top Area of Frustum of Cone

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

Curved Surface Area of Frustum of Cone given Volume Formula

LaTeX Go

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 Curved Surface Area of Frustum of Cone given Volume?

Curved Surface Area of Frustum of Cone given Volume calculator uses Curved Surface Area of Frustum of Cone = pi*(Top Radius of Frustum of Cone+Base Radius of Frustum of Cone)*sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone))))^2+(Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2) to calculate the Curved Surface Area of Frustum of Cone, The Curved Surface Area of Frustum of Cone given Volume formula is defined as the quantity of plane enclosed by curved surfaces (that is, top and bottom faces are excluded) of the Frustum of Cone, calculated using the volume, top radius and base radius of the Frustum of Cone. Curved Surface Area of Frustum of Cone is denoted by CSA symbol.

How to calculate Curved Surface Area of Frustum of Cone given Volume using this online calculator? To use this online calculator for Curved Surface Area of Frustum of Cone given Volume, enter Top Radius of Frustum of Cone (r_Top), Base Radius of Frustum of Cone (r_Base) & Volume of Frustum of Cone (V) and hit the calculate button. Here is how the Curved Surface Area of Frustum of Cone given Volume calculation can be explained with given input values -> 451.9868 = pi*(10+5)*sqrt(((3*1500)/(pi*(10^2+5^2+(10*5))))^2+(10-5)^2).

FAQ

What is Curved Surface Area of Frustum of Cone given Volume?

The Curved Surface Area of Frustum of Cone given Volume formula is defined as the quantity of plane enclosed by curved surfaces (that is, top and bottom faces are excluded) of the Frustum of Cone, calculated using the volume, top radius and base radius of the Frustum of Cone and is represented as CSA = pi*(r_Top+r_Base)*sqrt(((3*V)/(pi*(r_Top^2+r_Base^2+(r_Top*r_Base))))^2+(r_Top-r_Base)^2) or Curved Surface Area of Frustum of Cone = pi*(Top Radius of Frustum of Cone+Base Radius of Frustum of Cone)*sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone))))^2+(Top Radius of Frustum of Cone-Base Radius 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, 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 & Volume of Frustum of Cone is the quantity of three-dimensional space enclosed by the entire surface of the Frustum of the Cone.

How to calculate Curved Surface Area of Frustum of Cone given Volume?

The Curved Surface Area of Frustum of Cone given Volume formula is defined as the quantity of plane enclosed by curved surfaces (that is, top and bottom faces are excluded) of the Frustum of Cone, calculated using the volume, top radius and base radius of the Frustum of Cone is calculated using Curved Surface Area of Frustum of Cone = pi*(Top Radius of Frustum of Cone+Base Radius of Frustum of Cone)*sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone))))^2+(Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2). To calculate Curved Surface Area of Frustum of Cone given Volume, you need Top Radius of Frustum of Cone (r_Top), Base Radius of Frustum of Cone (r_Base) & Volume of Frustum of Cone (V). With our tool, you need to enter the respective value for Top Radius of Frustum of Cone, Base Radius of Frustum of Cone & Volume 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 Curved Surface Area of Frustum of Cone?

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

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

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