A right pyramid on a base 4cm square has a slant edge of 6cm. Calculate the volume of the pyramid
well, the height h = √(6^2-(4/2)^2)
and the volume, as usual, is 1/3 Bh
To calculate the volume of a pyramid, you can use the formula:
Volume = (1/3) × Base Area × Height
In this case, we're given the dimensions of the base square, but we need the base area. Since the base is a square, all four sides are equal.
Let's calculate the base area:
Base Area = side × side = 4 cm × 4 cm = 16 cm²
Next, we need the height of the pyramid. The height is the distance from the center of the base square to the apex (top) of the pyramid. However, we don't have the height directly given. Instead, we're given the slant edge, which we can find using the Pythagorean theorem.
The slant edge is the hypotenuse of the right triangle formed by the height, half of the base (2 cm), and the slant edge itself (6 cm):
Using the Pythagorean theorem:
slant edge² = height² + (1/2 base)²
6² = height² + 2²
36 = height² + 4
height² = 36 - 4
height² = 32
Taking the square root of both sides:
height = √32 cm
Now we have both the base area and the height, we can calculate the volume of the pyramid:
Volume = (1/3) × Base Area × Height
Volume = (1/3) × 16 cm² × √32 cm
To simplify the expression, we can calculate √32:
√32 ≈ 5.657
Volume = (1/3) × 16 cm² × 5.657 cm
Volume ≈ 30.056 cm³
Therefore, the volume of the pyramid is approximately 30.056 cubic centimeters.