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Total Surface Area of Cone given Volume and Height Formula

GoTotal Surface Area of Cone given Lateral Surface Area Formula

GoTotal Surface Area of Cone Formula

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Total Surface Area of Cone is defined as the total quantity of plane enclosed on the entire surface of the Cone. Check FAQs

TSA = \frac{3 \cdot V}{h} + π \cdot \sqrt{\frac{3 \cdot V}{π \cdot h} \cdot (h^{2} + \frac{3 \cdot V}{π \cdot h})}

TSA - Total Surface Area of Cone?V - Volume of Cone?h - Height of Cone?π - Archimedes' constant?

Total Surface Area of Cone given Volume and Height Example

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Here is how the Total Surface Area of Cone given Volume and Height equation looks like with Values.

Here is how the Total Surface Area of Cone given Volume and Height equation looks like with Units.

Here is how the Total Surface Area of Cone given Volume and Height equation looks like.

661.0679 = \frac{3 \cdot 520}{5} + 3.1416 \cdot \sqrt{\frac{3 \cdot 520}{3.1416 \cdot 5} \cdot (5^{2} + \frac{3 \cdot 520}{3.1416 \cdot 5})}

661.0679m² = \frac{3 \cdot 520m³}{5m} + 3.1416 \cdot \sqrt{\frac{3 \cdot 520m³}{3.1416 \cdot 5m} \cdot ({5m}^{2} + \frac{3 \cdot 520m³}{3.1416 \cdot 5m})}

661.0679 = \frac{3 \cdot 520}{5} + 3.1416 \cdot \sqrt{\frac{3 \cdot 520}{3.1416 \cdot 5} \cdot (5^{2} + \frac{3 \cdot 520}{3.1416 \cdot 5})}

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Total Surface Area of Cone given Volume and Height Solution

Follow our step by step solution on how to calculate Total Surface Area of Cone given Volume and Height?

FIRST Step Consider the formula

TSA = \frac{3 \cdot V}{h} + π \cdot \sqrt{\frac{3 \cdot V}{π \cdot h} \cdot (h^{2} + \frac{3 \cdot V}{π \cdot h})}

Next Step Substitute values of Variables

∴

TSA = \frac{3 \cdot 520m³}{5m} + π \cdot \sqrt{\frac{3 \cdot 520m³}{π \cdot 5m} \cdot ({5m}^{2} + \frac{3 \cdot 520m³}{π \cdot 5m})}

Next Step Substitute values of Constants

∴

TSA = \frac{3 \cdot 520m³}{5m} + 3.1416 \cdot \sqrt{\frac{3 \cdot 520m³}{3.1416 \cdot 5m} \cdot ({5m}^{2} + \frac{3 \cdot 520m³}{3.1416 \cdot 5m})}

Next Step Prepare to Evaluate

∴

TSA = \frac{3 \cdot 520}{5} + 3.1416 \cdot \sqrt{\frac{3 \cdot 520}{3.1416 \cdot 5} \cdot (5^{2} + \frac{3 \cdot 520}{3.1416 \cdot 5})}

Next Step Evaluate

∴

TSA = 661.06793421625m²

LAST Step Rounding Answer

∴

TSA = 661.0679m²

Total Surface Area of Cone given Volume and Height Formula Elements

Variables

Constants

Functions

Total Surface Area of Cone

Total Surface Area of Cone is defined as the total quantity of plane enclosed on the entire surface of the Cone.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Cone

Volume of Cone

Volume of Cone is defined as the total quantity of three-dimensional space enclosed by the entire surface of the Cone.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Cone

Height of Cone

Height of Cone is defined as the distance between the apex of the Cone to the center of its circular base.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height 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 Total Surface Area of Cone

Go Total Surface Area of Cone given Lateral Surface Area

TSA = LSA + (π \cdot {r Base}^{2})

Go Total Surface Area of Cone

TSA = π \cdot r Base \cdot (r Base + h Slant)

Go Total Surface Area of Cone given Base Area

TSA = (π \cdot r Base \cdot h Slant) + A Base

Go Total Surface Area of Cone given Lateral Surface Area and Base Area

TSA = LSA + A Base

How to Evaluate Total Surface Area of Cone given Volume and Height?

Total Surface Area of Cone given Volume and Height evaluator uses Total Surface Area of Cone = (3*Volume of Cone)/Height of Cone+pi*sqrt((3*Volume of Cone)/(pi*Height of Cone)*(Height of Cone^2+(3*Volume of Cone)/(pi*Height of Cone))) to evaluate the Total Surface Area of Cone, The Total Surface Area of Cone given Volume and Height formula is defined as the total quantity of plane enclosed on the entire surface of the Cone, and calculated using the height and volume of the Cone. Total Surface Area of Cone is denoted by TSA symbol.

How to evaluate Total Surface Area of Cone given Volume and Height using this online evaluator? To use this online evaluator for Total Surface Area of Cone given Volume and Height, enter Volume of Cone (V) & Height of Cone (h) and hit the calculate button.

FAQs on Total Surface Area of Cone given Volume and Height

What is the formula to find Total Surface Area of Cone given Volume and Height?

The formula of Total Surface Area of Cone given Volume and Height is expressed as Total Surface Area of Cone = (3*Volume of Cone)/Height of Cone+pi*sqrt((3*Volume of Cone)/(pi*Height of Cone)*(Height of Cone^2+(3*Volume of Cone)/(pi*Height of Cone))). Here is an example- 661.0679 = (3*520)/5+pi*sqrt((3*520)/(pi*5)*(5^2+(3*520)/(pi*5))).

How to calculate Total Surface Area of Cone given Volume and Height?

With Volume of Cone (V) & Height of Cone (h) we can find Total Surface Area of Cone given Volume and Height using the formula - Total Surface Area of Cone = (3*Volume of Cone)/Height of Cone+pi*sqrt((3*Volume of Cone)/(pi*Height of Cone)*(Height of Cone^2+(3*Volume of Cone)/(pi*Height of Cone))). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

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

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

Total Surface Area of Cone=Lateral Surface Area of Cone+(pi*Base Radius of Cone^2)
Total Surface Area of Cone=pi*Base Radius of Cone*(Base Radius of Cone+Slant Height of Cone)
Total Surface Area of Cone=(pi*Base Radius of Cone*Slant Height of Cone)+Base Area of Cone

Can the Total Surface Area of Cone given Volume and Height be negative?

No, the Total Surface Area of Cone given Volume and Height, measured in Area cannot be negative.

Which unit is used to measure Total Surface Area of Cone given Volume and Height?

Total Surface Area of Cone given Volume and Height 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 Total Surface Area of Cone given Volume and Height can be measured.

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Total Surface Area of Cone given Volume and Height Formula

​GoTotal Surface Area of Cone given Lateral Surface Area Formula

​GoTotal Surface Area of Cone Formula

Total Surface Area of Cone given Volume and Height Example

Total Surface Area of Cone given Volume and Height Solution

Total Surface Area of Cone given Volume and Height Formula Elements

Other Formulas to find Total Surface Area of Cone

How to Evaluate Total Surface Area of Cone given Volume and Height?

FAQs on Total Surface Area of Cone given Volume and Height

Variable Name

GoTotal Surface Area of Cone given Lateral Surface Area Formula

GoTotal Surface Area of Cone Formula