Curved Surface Area of Truncated Cone given Volume Calculator

✖Base Radius of Truncated Cone is the distance between the center and any point on the circumference of the base circular surface of the Truncated Cone.ⓘ Base Radius of Truncated Cone [r_Base]			+10% -10%
✖Top Radius of Truncated Cone is the distance between the center and any point on the circumference of the top circular surface of the Truncated Cone.ⓘ Top Radius of Truncated Cone [r_Top]			+10% -10%
✖Volume of Truncated Cone is the total quantity of three dimensional space enclosed by the entire surface of the Truncated Cone.ⓘ Volume of Truncated Cone [V]			+10% -10%

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

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Formula

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Curved Surface Area of Truncated Cone given Volume

Formula

`"CSA" = pi*("r"_{"Base"}+"r"_{"Top"})*sqrt(("r"_{"Base"}-"r"_{"Top"})^2+((3*"V")/(pi*("r"_{"Base"}^2+("r"_{"Base"}*"r"_{"Top"})+"r"_{"Top"}^2)))^2)`

Example

`"169.5185m²"=pi*("5m"+"2m")*sqrt(("5m"-"2m")^2+((3*"290m³")/(pi*(("5m")^2+("5m"*"2m")+("2m")^2)))^2)`

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Curved Surface Area of Truncated Cone given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Curved Surface Area of Truncated Cone - (Measured in Square Meter) - Curved Surface Area of Truncated Cone is the quantity of plane enclosed on curved surfaces (that is, top and bottom faces are excluded) of the Truncated Cone.
Base Radius of Truncated Cone - (Measured in Meter) - Base Radius of Truncated Cone is the distance between the center and any point on the circumference of the base circular surface of the Truncated Cone.
Top Radius of Truncated Cone - (Measured in Meter) - Top Radius of Truncated Cone is the distance between the center and any point on the circumference of the top circular surface of the Truncated Cone.
Volume of Truncated Cone - (Measured in Cubic Meter) - Volume of Truncated Cone is the total quantity of three dimensional space enclosed by the entire surface of the Truncated Cone.

STEP 1: Convert Input(s) to Base Unit

Base Radius of Truncated Cone: 5 Meter --> 5 Meter No Conversion Required
Top Radius of Truncated Cone: 2 Meter --> 2 Meter No Conversion Required
Volume of Truncated Cone: 290 Cubic Meter --> 290 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

CSA = pi*(r_Base+r_Top)*sqrt((r_Base-r_Top)^2+((3*V)/(pi*(r_Base^2+(r_Base*r_Top)+r_Top^2)))^2) --> pi*(5+2)*sqrt((5-2)^2+((3*290)/(pi*(5^2+(5*2)+2^2)))^2)

Evaluating ... ...

CSA = 169.518492234681

STEP 3: Convert Result to Output's Unit

169.518492234681 Square Meter --> No Conversion Required

FINAL ANSWER

169.518492234681 ≈ 169.5185 Square Meter <-- Curved Surface Area of Truncated Cone

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 3D Geometry » Cone » Truncated Cone » Surface Area of Truncated Cone » Curved Surface Area of Truncated Cone » Curved Surface Area of Truncated Cone given Volume

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Created by Nikhil

Mumbai University (DJSCE), Mumbai

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

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< 4 Curved Surface Area of Truncated Cone Calculators

Curved Surface Area of Truncated Cone given Volume

Go Curved Surface Area of Truncated Cone = pi*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)*sqrt((Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2+((3*Volume of Truncated Cone)/(pi*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2)))^2)

Curved Surface Area of Truncated Cone

Curved Surface Area of Truncated Cone given Total Surface Area

Go Curved Surface Area of Truncated Cone = Total Surface Area of Truncated Cone-pi*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2)

Curved Surface Area of Truncated Cone given Slant Height

Go Curved Surface Area of Truncated Cone = pi*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)*Slant Height of Truncated Cone

Curved Surface Area of Truncated Cone given Volume Formula

What is a Truncated Cone?

A Truncated Cone is basically a circular cone of which top is cut or 'truncated' by a horizontal plane. Or in another way, a Truncated Cone is formed when a smaller circular cone is cut from the top of a larger circular cone. The Truncated has two circular surfaces - one on top and another on the bottom, and a lateral curved surface. The slant height is the shortest distance between the two circles on the lateral surface, which is the surface without the circles.

How to Calculate Curved Surface Area of Truncated Cone given Volume?

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

How to calculate Curved Surface Area of Truncated Cone given Volume using this online calculator? To use this online calculator for Curved Surface Area of Truncated Cone given Volume, enter Base Radius of Truncated Cone (r_Base), Top Radius of Truncated Cone (r_Top) & Volume of Truncated Cone (V) and hit the calculate button. Here is how the Curved Surface Area of Truncated Cone given Volume calculation can be explained with given input values -> 169.5185 = pi*(5+2)*sqrt((5-2)^2+((3*290)/(pi*(5^2+(5*2)+2^2)))^2).

FAQ

What is Curved Surface Area of Truncated Cone given Volume?

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

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

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

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

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

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