Question

As shown on the diagram, a regular pyramid has a square base whose side measures 6 inches. If the altitude of the pyramid measures 12 inches, it’s volume, in cubic inches is

Answer 1

Answer:

144 in³

Step-by-step explanation:

The volume of a pyramid of base area A and height h is

V = (1/3)(A)(h).

Here,

V = (1/3)(6 in)²(12 in) = 144 in³

Answer 2

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  $\frac{1}{3} B_{A}h$.

The volume of the pyramid:

The volume of the pyramid is given by the formula:

$V=\frac{1}{3} B_{A}h$

Where,

$B_A$ 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,

$B_A =a^{2}$

⇒ $B_A=6^2$

⇒ $B_A=36$ sq. inches

Height of the pyramid h = 12 inches

On substituting the values in the formula,

$V=\frac{1}{3}B_Ah$

⇒ $\frac{1}{3}$ × 36 × 12

⇒ 4 × 36

⇒ 144 cubic inches

Therefore, the volume of the given pyramid is 144 cubic inches.

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