If a particular right square based pyramid has a volume of 63690 cubic meters and a height of thirty meters What is the number of meters in the length of the lateral height segment AB of a pyramid?

Answer 1

The formula for the volume of a pyramid such as you described would be: V = 1/3Ah where A is the area of the base (a square in this case) and h is the height of the pyramid. You know the volume and the height, so you can plug them into that formula to solve for A, the area of the square base: 63690 = 1/3A(30). A = 6369 square meters. Knowing the area of the square, and the fact that the formula for the area of a square is A = s2 where s is the length of a side, you can find the length of s by taking the square root of 6369. s = about 79.8 meters. The next steps will require some thinking about what that pyramid looks like and what the length of a lateral height segment would represent. Drawing a diagram often helps. If I understand correctly what you mean by "lateral height segment" of the pyramid, meaning the length of the segment from the center of a side at the bottom to the vertex at the top, that length would represent the hypotenuse of a right triangle whose legs are 30 meters (the inside height of the pyramid) and about 39.9 meters (half the length of a side, in other words the distance from the point at the center of the base to the center of the side). You can use the Pythagorean theorem to find that length:

c2 = a2 + b2

c2 = 302 + 39.92

c2 = 900 + 1592

c2 = 2492

c = 49.9 meters (approximately)