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:

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

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