Question

find the height of a pyramid with a volume of \\(128\text{ cm}^3\\) if the base is a square with a side length of \\(8\text{ cm}\\).

\\(\quad\text{ cm}\\)

Explanation:

Calculate the area of the square base

$$ B = s^2 = 8^2 = 64\text{ cm}^2 $$

Set up the volume formula for a pyramid

$$ V = \frac{1}{3} \cdot B \cdot h $$

$$ 128 = \frac{1}{3} \cdot 64 \cdot h $$

Solve for the height

$$ 384 = 64 \cdot h $$

$$ h = \frac{384}{64} = 6\text{ cm} $$

Answer:

Find the height of a pyramid with a volume of \(128\text{ cm}^3\) if the base is a square with a side length of \(8\text{ cm}\).

<blank>6</blank> cm