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  d2=a2+a2 d2=2 a2 d=2⋅ a=2⋅ 4≐4 2 cm≐5.6569 cm  s2=(d/2)2+h2  h=s2−(d/2)2=62−(5.6569/2)2≐2 7 cm≐5.2915 cm  V=13⋅ a2⋅ h=13⋅ 42⋅ 5.2915≐28.2213≐28.221 cm3a=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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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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