What is the volume of the pyramid to the nearest whole unit
9 yd 9 yd 14 yd
1. 1,134 yd3
2. 567 yd 3
3. 378 yd 3
4. 285 yd 3
explain why
The formula for the volume of a pyramid is V = (1/3)Bh, where B is the area of the base and h is the height.
In this case, the base is a square with side length 9 yards, so B = 9^2 = 81 square yards. The height of the pyramid is given as 14 yards.
Plugging these values into the formula, we get:
V = (1/3)(81)(14) = 3(81)(2) = 486 cubic yards
Rounding to the nearest whole unit, the volume of the pyramid is 486 cubic yards, which corresponds to answer choice 2.
perhaps 14 is the slant height
4.5^2 + h^2 = 14^2
20.25 + h^2 = 196
h^2 = 175.75
h = 13.26
then
vol = (1/3) (81)(13.26) = 358
Maybe number 3 ?
Yes, that calculation and reasoning are correct. The slant height of the pyramid can be found using the Pythagorean theorem with half the diagonal of the base (4.5 yards) and the given height (unknown).
Solving for h gives h ≈ 13.26 yards.
Using the formula for the volume of a pyramid, we can calculate:
V = (1/3)(81)(13.26) ≈ 358 cubic yards
Rounding to the nearest whole unit, we get 358 cubic yards, which corresponds to answer choice 3.
To find the volume of a pyramid, you can use the formula V = (1/3) * base area * height.
In this case, the given dimensions for the pyramid base are 9 yards and 9 yards, and the height is 14 yards.
First, let's calculate the base area:
Base area = length * width
Base area = 9 yards * 9 yards = 81 square yards
Now, substitute the values into the formula to find the volume:
V = (1/3) * base area * height
V = (1/3) * 81 square yards * 14 yards
V = (1/3) * 1134 cubic yards
V ≈ 378 cubic yards (rounded to the nearest whole unit)
Therefore, the volume of the pyramid is approximately 378 cubic yards. So, the answer is 3. 378 yd3.