Question

A square pyramid has side lengths of 5 yards and a height of 6 yards. An oblique cone has the same height and equal volume.

Part a: What is the volume of the pyramid? Show all necessary steps.
Part b: What is the radius of the cone? Round to the nearest tenth of a yard. Show all necessary steps.

Answer 1

The volume of the square pyramid with side lengths of 5 yards and a height of 6 yards is 50 cubic yards. The radius of the oblique cone with the same volume is approximately 2.82 yards.

Step-by-step explanation:

Part a:

To find the volume of a square pyramid, we can use the formula V = (1/3) * base area * height. The base area of a square is found by multiplying the side length by itself. So, the base area of the pyramid is 5 yards * 5 yards = 25 square yards. Substituting the values into the formula, we get V = (1/3) * 25 square yards * 6 yards = 50 cubic yards.

Part b:

To find the radius of the oblique cone, we can use the formula V = (1/3) * π * radius^2 * height. Since the volume of the cone is equal to the volume of the pyramid, we can set up the equation 50 cubic yards = (1/3) * π * radius^2 * 6 yards. Solving for the radius, we get radius^2 = (50 * 3) / (π * 6) = 7.95. Taking the square root of both sides, we find that the radius is approximately 2.82 yards.