A regular pyramid has a square base. The volume of the pyramid is 600 and its height is 17. If the vertex of the pyramid is V and the base is the square ABCD, the length of VA is approximately ______.18.534.524.529.5
Question
A regular pyramid has a square base. The volume of the pyramid is 600 and its height is 17. If the vertex of the pyramid is V and the base is the square ABCD, the length of VA is approximately ______.18.534.524.529.5
Solution
To find the length of VA, we first need to find the length of the side of the base square (s). We know that the volume (V) of a pyramid is given by the formula V = 1/3 * base area * height. In this case, the base is a square, so the area is s^2.
So, we have:
600 = 1/3 * s^2 * 17
Solving for s, we get:
s^2 = (600 * 3) / 17
s^2 = 105.882
Taking the square root of both sides, we get:
s = 10.29 (approximately)
Now, to find VA, we need to use the Pythagorean theorem. The length of VA is the hypotenuse of a right triangle, where one side is the height of the pyramid (17) and the other side is half the length of the base square (s/2 = 10.29/2 = 5.145).
So, we have:
VA^2 = 17^2 + 5.145^2
VA^2 = 289 + 26.48
VA^2 = 315.48
Taking the square root of both sides, we get:
VA = 17.76 (approximately)
So, the length of VA is approximately 17.76.
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