Two square pyramids have the same volume. For the first pyramid, the side length of the base is 8 cm and the height is 12 cm. The second pyramid has a height of 14 cm. What is the side length of the base of the second pyramid? Round to the nearest tenth!!!!

1 answer

To find the side length of the base of the second pyramid, we can use the formula for the volume of a square pyramid, which is V = (1/3) * (base area) * height.

Since the two pyramids have the same volume, we can set up an equation with their respective volume formulas:

(1/3) * (8^2) * 12 = (1/3) * x^2 * 14

Simplifying this equation, we get:

(64) * 12 = (14) * x^2

768 = 14x^2

Divide both sides by 14 to isolate x^2:

x^2 = 768 / 14

x^2 = 54.86

x = sqrt(54.86)

x ≈ 7.4

Therefore, the side length of the base of the second pyramid is approximately 7.4 cm.