The volume of a pyramid is given by the formula V = (1/3) * base area * height, where the base area is the area of the base of the pyramid and the height is the perpendicular distance from the base to the apex.
In this case, the base of the pyramid is a square with side length 4 cm, so the base area is 4 cm * 4 cm = 16 cm^2.
The height of the pyramid can be found using the Pythagorean theorem. The height, slant edge, and half the side length of the base form a right triangle, so we have:
height^2 + (2 cm)^2 = (6 cm)^2
height^2 + 4 cm^2 = 36 cm^2
height^2 = 32 cm^2
height = √32 cm = 4√2 cm
Now we can plug the base area and height into the volume formula:
V = (1/3) * 16 cm^2 * 4√2 cm
V = (16√2) / 3 cm^3
V ≈ 30.75 cm^3
Therefore, the volume of the pyramid is approximately 30.75 cm^3.
a right pyramid on a base 4 cm square has a slant edge of 6 cm. Calculate the volume of the pyramid
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