The volume of the given pyramid with a square base whose side measures 6 inches and the altitude of the pyramid measures 12 inches is 144 cubic inches. The value is obtained by applying the formula for the volume of the pyramid as [tex]\frac{1}{3} B_{A}h[/tex].
The volume of the pyramid:
The volume of the pyramid is given by the formula:
[tex]V=\frac{1}{3} B_{A}h[/tex]
Where,
[tex]B_A[/tex] is the area of the base of the pyramid and
h is the height or altitude of the pyramid
Calculating the Volume:
As shown in the diagram,
The pyramid has a square base whose side measures 6 inches and the altitude of the pyramid is 12 inches
Thus,
Area of the square base,
[tex]B_A =a^{2}[/tex]
⇒ [tex]B_A=6^2[/tex]
⇒ [tex]B_A=36[/tex] sq. inches
Height of the pyramid h = 12 inches
On substituting the values in the formula,
[tex]V=\frac{1}{3}B_Ah[/tex]
⇒ [tex]\frac{1}{3}[/tex] × 36 × 12
⇒ 4 × 36
⇒ 144 cubic inches
Therefore, the volume of the given pyramid is 144 cubic inches.
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