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

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

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

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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. Check FAQs

CSA = π \cdot (r Top + \sqrt{\frac{A Base}{π}}) \cdot \sqrt{{(\frac{3 \cdot V}{π \cdot ({r Top}^{2} + \frac{A Base}{π} + (\sqrt{\frac{A Base}{π}} \cdot r Top))})}^{2} + {(r Top - \sqrt{\frac{A Base}{π}})}^{2}}

CSA - Curved Surface Area of Frustum of Cone?r_Top - Top Radius of Frustum of Cone?A_Base - Base Area of Frustum of Cone?V - Volume of Frustum of Cone?π - Archimedes' constant?

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

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Here is how the Curved Surface Area of Frustum of Cone given Volume and Base Area equation looks like with Units.

Here is how the Curved Surface Area of Frustum of Cone given Volume and Base Area equation looks like.

450.5009 = 3.1416 \cdot (10 + \sqrt{\frac{80}{3.1416}}) \cdot \sqrt{{(\frac{3 \cdot 1500}{3.1416 \cdot (10^{2} + \frac{80}{3.1416} + (\sqrt{\frac{80}{3.1416}} \cdot 10))})}^{2} + {(10 - \sqrt{\frac{80}{3.1416}})}^{2}}

450.5009m² = 3.1416 \cdot (10m + \sqrt{\frac{80m²}{3.1416}}) \cdot \sqrt{{(\frac{3 \cdot 1500m³}{3.1416 \cdot ({10m}^{2} + \frac{80m²}{3.1416} + (\sqrt{\frac{80m²}{3.1416}} \cdot 10m))})}^{2} + {(10m - \sqrt{\frac{80m²}{3.1416}})}^{2}}

450.5009 = 3.1416 \cdot (10 + \sqrt{\frac{80}{3.1416}}) \cdot \sqrt{{(\frac{3 \cdot 1500}{3.1416 \cdot (10^{2} + \frac{80}{3.1416} + (\sqrt{\frac{80}{3.1416}} \cdot 10))})}^{2} + {(10 - \sqrt{\frac{80}{3.1416}})}^{2}}

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

Follow our step by step solution on how to calculate Curved Surface Area of Frustum of Cone given Volume and Base Area?

FIRST Step Consider the formula

CSA = π \cdot (r Top + \sqrt{\frac{A Base}{π}}) \cdot \sqrt{{(\frac{3 \cdot V}{π \cdot ({r Top}^{2} + \frac{A Base}{π} + (\sqrt{\frac{A Base}{π}} \cdot r Top))})}^{2} + {(r Top - \sqrt{\frac{A Base}{π}})}^{2}}

Next Step Substitute values of Variables

∴

CSA = π \cdot (10m + \sqrt{\frac{80m²}{π}}) \cdot \sqrt{{(\frac{3 \cdot 1500m³}{π \cdot ({10m}^{2} + \frac{80m²}{π} + (\sqrt{\frac{80m²}{π}} \cdot 10m))})}^{2} + {(10m - \sqrt{\frac{80m²}{π}})}^{2}}

Next Step Substitute values of Constants

∴

CSA = 3.1416 \cdot (10m + \sqrt{\frac{80m²}{3.1416}}) \cdot \sqrt{{(\frac{3 \cdot 1500m³}{3.1416 \cdot ({10m}^{2} + \frac{80m²}{3.1416} + (\sqrt{\frac{80m²}{3.1416}} \cdot 10m))})}^{2} + {(10m - \sqrt{\frac{80m²}{3.1416}})}^{2}}

Next Step Prepare to Evaluate

∴

CSA = 3.1416 \cdot (10 + \sqrt{\frac{80}{3.1416}}) \cdot \sqrt{{(\frac{3 \cdot 1500}{3.1416 \cdot (10^{2} + \frac{80}{3.1416} + (\sqrt{\frac{80}{3.1416}} \cdot 10))})}^{2} + {(10 - \sqrt{\frac{80}{3.1416}})}^{2}}

Next Step Evaluate

∴

CSA = 450.500938896687m²

LAST Step Rounding Answer

∴

CSA = 450.5009m²

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

Variables

Constants

Functions

Curved Surface Area of Frustum of Cone

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.

Symbol: CSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Curved Surface Area of Frustum of Cone

Top Radius of Frustum of Cone

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.

Symbol: r_Top

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Top Radius of Frustum of Cone

Base Area of Frustum of 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.

Symbol: A_Base

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Base Area of Frustum of Cone

Volume of Frustum of Cone

Volume of Frustum of Cone is the quantity of three-dimensional space enclosed by the entire surface of the Frustum of the Cone.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Frustum of Cone

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sqrt(Number)

Other Formulas to find Curved Surface Area of Frustum of Cone

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

CSA = π \cdot (2 \cdot r Top - \sqrt{{h Slant}^{2} - h^{2}}) \cdot h Slant

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

CSA = π \cdot (\sqrt{{h Slant}^{2} - h^{2}} + 2 \cdot r Base) \cdot h Slant

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

CSA = π \cdot (\sqrt{\frac{A Top}{π}} + \sqrt{\frac{A Base}{π}}) \cdot h Slant

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

CSA = π \cdot (\sqrt{{h Slant}^{2} - h^{2}} + 2 \cdot \sqrt{\frac{A Base}{π}}) \cdot h Slant

How to Evaluate Curved Surface Area of Frustum of Cone given Volume and Base Area?

Curved Surface Area of Frustum of Cone given Volume and Base Area evaluator uses 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) to evaluate the Curved Surface Area of Frustum of Cone, The Curved Surface Area of Frustum of Cone given Volume 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 volume, top radius and base area of the Frustum of Cone. Curved Surface Area of Frustum of Cone is denoted by CSA symbol.

How to evaluate Curved Surface Area of Frustum of Cone given Volume and Base Area using this online evaluator? To use this online evaluator for Curved Surface Area of Frustum of Cone given Volume and Base Area, enter Top Radius of Frustum of Cone (r_Top), Base Area of Frustum of Cone (A_Base) & Volume of Frustum of Cone (V) and hit the calculate button.

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

What is the formula to find Curved Surface Area of Frustum of Cone given Volume and Base Area?

The formula of Curved Surface Area of Frustum of Cone given Volume and Base Area is expressed as 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). Here is an example- 450.5009 = pi*(10+sqrt(80/pi))*sqrt(((3*1500)/(pi*(10^2+80/pi+(sqrt(80/pi)*10))))^2+(10-sqrt(80/pi))^2).

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

With Top Radius of Frustum of Cone (r_Top), Base Area of Frustum of Cone (A_Base) & Volume of Frustum of Cone (V) we can find Curved Surface Area of Frustum of Cone given Volume and Base Area using the formula - 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). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Curved Surface Area of Frustum of Cone?

Here are the different ways to Calculate Curved Surface Area of Frustum of Cone-

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

Can the Curved Surface Area of Frustum of Cone given Volume and Base Area be negative?

No, the Curved Surface Area of Frustum of Cone given Volume and Base Area, measured in Area cannot be negative.

Which unit is used to measure Curved Surface Area of Frustum of Cone given Volume and Base Area?

Curved Surface Area of Frustum of Cone given Volume and Base Area is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Curved Surface Area of Frustum of Cone given Volume and Base Area can be measured.

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

​GoCurved Surface Area of Frustum of Cone given Slant Height, Height and Top Radius Formula

​GoCurved Surface Area of Frustum of Cone given Slant Height, Height and Base Radius Formula

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

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

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

Other Formulas to find Curved Surface Area of Frustum of Cone

How to Evaluate Curved Surface Area of Frustum of Cone given Volume and Base Area?

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

Variable Name

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

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