A pyramid has a height of 12 centimeters and a square base. If the valume of the pyramid is 256 cubic centimeters, how many centimeters are in the length aof one side of its base?

Options

A. `8`
B. `16`
C. `32`
D. `(8)/(sqrt(3))`

Answer

To find the length of one side of the base of the pyramid, we can use the formula for the volume of a pyramid. The volume \( V \) of a pyramid is given by the formula:

\[ V = \frac{1}{3} \times \text{Area of base} \times \text{Height} \]

Given:
- Height \( h = 12 \) cm
- Volume \( V = 256 \) cm³

We need to find the area of the base first. Since the base is a square, let the length of one side of the base be \( s \). The area of the base \( A \) can be expressed as:

\[ A = s^2 \]

Now substituting the known values into the volume formula:

\[ 256 = \frac{1}{3} \times A \times 12 \]

Substituting \( A = s^2 \):

\[ 256 = \frac{1}{3} \times s^2 \times 12 \]

Now, simplify the equation:

\[ 256 = 4s^2 \]

Next, we can solve for \( s^2 \):

\[ s^2 = \frac{256}{4} \]

Calculating the right-hand side:

\[ s^2 = 64 \]

Now, to find \( s \), we take the square root of both sides:

\[ s = \sqrt{64} \]

Calculating the square root:

\[ s = 8 \text{ cm} \]

Thus, the length of one side of the base of the pyramid is \( 8 \) centimeters.