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Volume of Square Pyramid given Slant Height Formula

GoVolume of Square Pyramid Formula

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Volume of Square Pyramid is the total quantity of three-dimensional space enclosed by the surface of the Square Pyramid. Check FAQs

V = \frac{1}{3} \cdot {l e(Base)}^{2} \cdot \sqrt{{h slant}^{2} - \frac{{l e(Base)}^{2}}{4}}

V - Volume of Square Pyramid?l_e(Base) - Edge Length of Base of Square Pyramid?h_slant - Slant Height of Square Pyramid?

Volume of Square Pyramid given Slant Height Example

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Here is how the Volume of Square Pyramid given Slant Height equation looks like with Values.

Here is how the Volume of Square Pyramid given Slant Height equation looks like with Units.

Here is how the Volume of Square Pyramid given Slant Height equation looks like.

506.6228 = \frac{1}{3} \cdot 10^{2} \cdot \sqrt{16^{2} - \frac{10^{2}}{4}}

506.6228m³ = \frac{1}{3} \cdot {10m}^{2} \cdot \sqrt{{16m}^{2} - \frac{{10m}^{2}}{4}}

506.6228 = \frac{1}{3} \cdot 10^{2} \cdot \sqrt{16^{2} - \frac{10^{2}}{4}}

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Volume of Square Pyramid given Slant Height Solution

Follow our step by step solution on how to calculate Volume of Square Pyramid given Slant Height?

FIRST Step Consider the formula

V = \frac{1}{3} \cdot {l e(Base)}^{2} \cdot \sqrt{{h slant}^{2} - \frac{{l e(Base)}^{2}}{4}}

Next Step Substitute values of Variables

∴

V = \frac{1}{3} \cdot {10m}^{2} \cdot \sqrt{{16m}^{2} - \frac{{10m}^{2}}{4}}

Next Step Prepare to Evaluate

∴

V = \frac{1}{3} \cdot 10^{2} \cdot \sqrt{16^{2} - \frac{10^{2}}{4}}

Next Step Evaluate

∴

V = 506.622805119022m³

LAST Step Rounding Answer

∴

V = 506.6228m³

Volume of Square Pyramid given Slant Height Formula Elements

Variables

Functions

Volume of Square Pyramid

Volume of Square Pyramid is the total quantity of three-dimensional space enclosed by the surface of the Square Pyramid.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Square Pyramid

Edge Length of Base of Square Pyramid

Edge Length of Base of Square Pyramid is the length of the straight line connecting any two adjacent vertices of the base of the Square Pyramid.

Symbol: l_e(Base)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of Base of Square Pyramid

Slant Height of Square Pyramid

Slant Height of Square Pyramid is the length measured along the lateral face from the base to the apex of the Square Pyramid along the center of the face.

Symbol: h_slant

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Slant Height of Square Pyramid

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 Volume of Square Pyramid

Go Volume of Square Pyramid

V = \frac{{l e(Base)}^{2} \cdot h}{3}

Other formulas in Volume of Square Pyramid category

Go Lateral Edge Length of Square Pyramid

l e(Lateral) = \sqrt{\frac{{l e(Base)}^{2}}{2} + h^{2}}

Go Slant Height of Square Pyramid

h slant = \sqrt{\frac{{l e(Base)}^{2}}{4} + h^{2}}

Go Base Area of Square Pyramid

A Base = {l e(Base)}^{2}

Go Base Angle of Square Pyramid

∠ Base = \arccos (\frac{{(\frac{l e(Base)}{2})}^{2} + {h slant}^{2} - h^{2}}{l e(Base) \cdot h slant})

How to Evaluate Volume of Square Pyramid given Slant Height?

Volume of Square Pyramid given Slant Height evaluator uses Volume of Square Pyramid = 1/3*Edge Length of Base of Square Pyramid^2*sqrt(Slant Height of Square Pyramid^2-(Edge Length of Base of Square Pyramid^2)/4) to evaluate the Volume of Square Pyramid, Volume of Square Pyramid given Slant Height formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Square Pyramid and is calculated using the slant height of the Square Pyramid. Volume of Square Pyramid is denoted by V symbol.

How to evaluate Volume of Square Pyramid given Slant Height using this online evaluator? To use this online evaluator for Volume of Square Pyramid given Slant Height, enter Edge Length of Base of Square Pyramid (l_e(Base)) & Slant Height of Square Pyramid (h_slant) and hit the calculate button.

FAQs on Volume of Square Pyramid given Slant Height

What is the formula to find Volume of Square Pyramid given Slant Height?

The formula of Volume of Square Pyramid given Slant Height is expressed as Volume of Square Pyramid = 1/3*Edge Length of Base of Square Pyramid^2*sqrt(Slant Height of Square Pyramid^2-(Edge Length of Base of Square Pyramid^2)/4). Here is an example- 506.6228 = 1/3*10^2*sqrt(16^2-(10^2)/4).

How to calculate Volume of Square Pyramid given Slant Height?

With Edge Length of Base of Square Pyramid (l_e(Base)) & Slant Height of Square Pyramid (h_slant) we can find Volume of Square Pyramid given Slant Height using the formula - Volume of Square Pyramid = 1/3*Edge Length of Base of Square Pyramid^2*sqrt(Slant Height of Square Pyramid^2-(Edge Length of Base of Square Pyramid^2)/4). This formula also uses Square Root Function function(s).

What are the other ways to Calculate Volume of Square Pyramid?

Here are the different ways to Calculate Volume of Square Pyramid-

Volume of Square Pyramid=(Edge Length of Base of Square Pyramid^2*Height of Square Pyramid)/3

Can the Volume of Square Pyramid given Slant Height be negative?

No, the Volume of Square Pyramid given Slant Height, measured in Volume cannot be negative.

Which unit is used to measure Volume of Square Pyramid given Slant Height?

Volume of Square Pyramid given Slant Height is usually measured using the Cubic Meter[m³] for Volume. Cubic Centimeter[m³], Cubic Millimeter[m³], Liter[m³] are the few other units in which Volume of Square Pyramid given Slant Height can be measured.

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Volume of Square Pyramid given Slant Height Formula

​GoVolume of Square Pyramid Formula

Volume of Square Pyramid given Slant Height Example

Volume of Square Pyramid given Slant Height Solution

Volume of Square Pyramid given Slant Height Formula Elements

Other Formulas to find Volume of Square Pyramid

Other formulas in Volume of Square Pyramid category

How to Evaluate Volume of Square Pyramid given Slant Height?

FAQs on Volume of Square Pyramid given Slant Height

Variable Name

GoVolume of Square Pyramid Formula