The height of a square-based pyramid is 12cm. The volume of the pyramid is 676 cubic centimeters. How long is each side of the square base?
To find the length of each side of the square base, we can use the formula for the volume of a square-based pyramid:
Volume = (1/3) * base area * height
Given that the volume is 676 cubic centimeters and the height is 12 cm, we can rearrange the formula to solve for the base area:
Base area = 3 * Volume / height
Base area = 3 * 676 / 12
Base area = 169 square centimeters
Since the base of the pyramid is a square, we know that the length of each side of the square base is equal. Let's denote the length of each side as x. Then we have:
x^2 = 169
x = √169
x = 13
Therefore, each side of the square base is 13 cm long.