Height of a pyramid on a square is 18cm if the volume of the pyramid is 294cm³ find the length of a side of a base
To find the length of a side of the base of the pyramid, we can use the formula for the volume of a pyramid:
Volume = (1/3) * base_area * height
In this case, the volume of the pyramid is 294cm³ and the height is 18cm. Let's assume the length of a side of the base is x. Since the base is a square, the base area can be calculated as x².
Plugging these values into the formula, we have:
294 = (1/3) * x² * 18
To solve for x, we can simplify the equation by multiplying both sides by 3:
882 = x² * 18
Divide both sides by 18 to isolate x²:
x² = 882 / 18
Simplify the right side:
x² = 49
Now take the square root of both sides to solve for x:
x = √49
x = 7
Therefore, the length of a side of the base of the pyramid is 7cm.
To find the length of a side of the base of the pyramid, we can use the formula for the volume of a pyramid:
Volume = (1/3) * base area * height
Given that the volume of the pyramid is 294 cm³ and the height is 18 cm, we can rearrange the formula to solve for the base area:
base area = (3 * Volume) / height
Substituting the given values:
base area = (3 * 294 cm³) / 18 cm
base area = 882 cm² / 18 cm
base area ≈ 49 cm²
Since the base of the pyramid is square, the length of a side of the base is equal to the square root of the base area. Therefore, the length of a side of the base is approximately √49 cm, which is 7 cm.