Curved Surface Area of Frustum of Cone given Slant Height, Height and Base Area 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%
✖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 [A_Base]			+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 Slant Height, Height and Base Area [CSA]

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

Formula

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

Example

`"401.9376m²"=pi*(sqrt(("9m")^2-("8m")^2)+2*sqrt("80m²"/pi))*"9m"`

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

STEP 0: Pre-Calculation Summary

Formula Used

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
CSA = pi*(sqrt(h_Slant^2-h^2)+2*sqrt(A_Base/pi))*h_Slant
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.
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 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.

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 Area of Frustum of Cone: 80 Square Meter --> 80 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

CSA = pi*(sqrt(h_Slant^2-h^2)+2*sqrt(A_Base/pi))*h_Slant --> pi*(sqrt(9^2-8^2)+2*sqrt(80/pi))*9

Evaluating ... ...

CSA = 401.937630518369

STEP 3: Convert Result to Output's Unit

401.937630518369 Square Meter --> No Conversion Required

FINAL ANSWER

401.937630518369 ≈ 401.9376 Square Meter <-- Curved Surface Area of Frustum of Cone

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 3D Geometry » Frustum of Cone » Surface Area of Frustum of Cone » Curved Surface Area of Frustum of Cone » Curved Surface Area of Frustum of Cone given Slant Height, Height and Base Area

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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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< 20 Curved Surface Area of Frustum of Cone Calculators

Curved Surface Area of Frustum of Cone given Volume, Top Area and Base Area

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))*sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Area of Frustum of Cone/pi+Base Area of Frustum of Cone/pi+(sqrt(Top Area of Frustum of Cone/pi)*sqrt(Base Area of Frustum of Cone/pi)))))^2+(sqrt(Top Area of Frustum of Cone/pi)-sqrt(Base Area of Frustum of Cone/pi))^2)

Curved Surface Area of Frustum of Cone given Volume and Base Area

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

Curved Surface Area of Frustum of Cone given Volume and Top Area

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

Curved Surface Area of Frustum of Cone given Volume

Go 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)

Curved Surface Area of Frustum of Cone given Base Area and Top Area

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

Curved Surface Area of Frustum of Cone given Base Area

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

Curved Surface Area of Frustum of Cone given Top Area

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

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

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, Height and Top Area

Go Curved Surface Area of Frustum of Cone = pi*(2*sqrt(Top Area of Frustum of Cone/pi)-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

Go Curved 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)

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

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

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

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

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

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

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

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

Curved Surface Area of Frustum of Cone given Total Surface Area

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

Curved Surface Area of Frustum of Cone given Total Surface Area and Base Area

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

Curved Surface Area of Frustum of Cone given Total Surface Area and Top Area

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

Curved Surface Area of Frustum of Cone given Slant Height

Go Curved 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

Curved Surface Area of Frustum of Cone given Total Surface Area, Top Area and Base Area

Go Curved Surface Area of Frustum of Cone = Total Surface Area of Frustum of Cone-(Base Area of Frustum of Cone+Top Area of Frustum of Cone)

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

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 Slant Height, Height and Base Area?

Curved Surface Area of Frustum of Cone given Slant Height, Height and Base Area calculator uses 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 to calculate the Curved Surface Area of Frustum of Cone, The Curved Surface Area of Frustum of Cone given Slant Height, Height and Base Area 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 slant height, height and base area 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 Slant Height, Height and Base Area using this online calculator? To use this online calculator for Curved Surface Area of Frustum of Cone given Slant Height, Height and Base Area, enter Slant Height of Frustum of Cone (h_Slant), Height of Frustum of Cone (h) & Base Area of Frustum of Cone (A_Base) and hit the calculate button. Here is how the Curved Surface Area of Frustum of Cone given Slant Height, Height and Base Area calculation can be explained with given input values -> 401.9376 = pi*(sqrt(9^2-8^2)+2*sqrt(80/pi))*9.

FAQ

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

The Curved Surface Area of Frustum of Cone given Slant Height, Height and Base Area 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 slant height, height and base area of the Frustum of Cone and is represented as CSA = pi*(sqrt(h_Slant^2-h^2)+2*sqrt(A_Base/pi))*h_Slant or 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. 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 & 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.

How to calculate Curved Surface Area of Frustum of Cone given Slant Height, Height and Base Area?

The Curved Surface Area of Frustum of Cone given Slant Height, Height and Base Area 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 slant height, height and base area of the Frustum of Cone is calculated using 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. To calculate Curved Surface Area of Frustum of Cone given Slant Height, Height and Base Area, you need Slant Height of Frustum of Cone (h_Slant), Height of Frustum of Cone (h) & Base Area of Frustum of Cone (A_Base). With our tool, you need to enter the respective value for Slant Height of Frustum of Cone, Height of Frustum of Cone & Base Area 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 Slant Height of Frustum of Cone, Height of Frustum of Cone & Base Area of Frustum of Cone. We can use 19 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
Curved Surface Area of Frustum of Cone = pi*(2*sqrt(Top Area of Frustum of Cone/pi)-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*(Top Radius of Frustum of Cone+sqrt(Base Area of Frustum of Cone/pi))*sqrt((Top Radius of Frustum of Cone-sqrt(Base Area of Frustum of Cone/pi))^2+Height of Frustum of Cone^2)
Curved Surface Area of Frustum of Cone = pi*(sqrt(Top Area of Frustum of Cone/pi)+sqrt(Base Area of Frustum of Cone/pi))*sqrt((sqrt(Top Area of Frustum of Cone/pi)-sqrt(Base Area of Frustum of Cone/pi))^2+Height of Frustum of Cone^2)
Curved Surface Area of Frustum of Cone = pi*(sqrt(Top Area of Frustum of Cone/pi)+Base Radius of Frustum of Cone)*sqrt((sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2+Height of Frustum of Cone^2)
Curved Surface Area of Frustum of Cone = pi*(Top Radius of Frustum of Cone+sqrt(Base Area of Frustum of Cone/pi))*Slant Height of Frustum of Cone
Curved Surface Area of Frustum of Cone = pi*(sqrt(Top Area of Frustum of Cone/pi)+Base Radius of Frustum of Cone)*Slant Height of Frustum of Cone
Curved Surface Area of Frustum of Cone = Total Surface Area of Frustum of Cone-(pi*Top Radius of Frustum of Cone^2)-Base Area of Frustum of Cone
Curved Surface Area of Frustum of Cone = Total Surface Area of Frustum of Cone-(pi*Base Radius of Frustum of Cone^2)-Top Area of Frustum of Cone
Curved Surface Area of Frustum of Cone = Total Surface Area of Frustum of Cone-(Base Area of Frustum of Cone+Top Area 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))*sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Area of Frustum of Cone/pi+Base Area of Frustum of Cone/pi+(sqrt(Top Area of Frustum of Cone/pi)*sqrt(Base Area of Frustum of Cone/pi)))))^2+(sqrt(Top Area of Frustum of Cone/pi)-sqrt(Base Area of Frustum of Cone/pi))^2)
Curved Surface Area of Frustum of Cone = pi*(sqrt(Top Area of Frustum of Cone/pi)+Base Radius of Frustum of Cone)*sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Area of Frustum of Cone/pi+Base Radius of Frustum of Cone^2+(sqrt(Top Area of Frustum of Cone/pi)*Base Radius of Frustum of Cone))))^2+(sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2)
Curved Surface Area of Frustum of Cone = pi*(Top Radius of Frustum of Cone+sqrt(Base Area of Frustum of Cone/pi))*sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Radius of Frustum of Cone^2+Base Area of Frustum of Cone/pi+(sqrt(Base Area of Frustum of Cone/pi)*Top Radius of Frustum of Cone))))^2+(Top Radius of Frustum of Cone-sqrt(Base Area of Frustum of Cone/pi))^2)
Curved 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)
Curved 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
Curved Surface Area of Frustum of Cone = Total Surface Area of Frustum of Cone-(pi*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2))
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)

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