# Right pyramid

A right pyramid on a base 4 cm square has a slant edge of 6 cm. Calculate the volume of the pyramid.

Result

V =  28.221 cm3

#### Solution:

$a = 4 \ cm \ \\ s = 6 \ cm \ \\ \ \\ d^2 = a^2 + a^2 \ \\ d^2 = 2 \ a^2 \ \\ d = \sqrt{ 2 } \cdot \ a = \sqrt{ 2 } \cdot \ 4 = 4 \ \sqrt{ 2 } \ cm \doteq 5.6569 \ cm \ \\ \ \\ s^2 = (d/2)^2 + h^2 \ \\ \ \\ h = \sqrt{ s^2-(d/2)^2 } = \sqrt{ 6^2-(5.6569/2)^2 } = 2 \ \sqrt{ 7 } \ cm \doteq 5.2915 \ cm \ \\ \ \\ V = \dfrac{ 1 }{ 3 } \cdot \ a^2 \cdot \ h = \dfrac{ 1 }{ 3 } \cdot \ 4^2 \cdot \ 5.2915 \doteq 28.2213 = 28.221 \ cm^3$

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#### Following knowledge from mathematics are needed to solve this word math problem:

Tip: Our volume units converter will help you with the conversion of volume units. Pythagorean theorem is the base for the right triangle calculator.

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