Question

Think of a sphere of radius r as being made up of a large number k of congruent small square-based pyramids. Let the area of each square base be B. What is the volume of one pyramid in terms of r, k, and B?

a) V = r^3
b) V = (r^2 * B) / k
c) V = B / (r^2 * k)
d) V = (r * B) / k

Answer 1

The volume of one pyramid in terms of r, k, and B is (r * B) / k.

Step-by-step explanation:

The volume of one pyramid in terms of r, k, and B can be found using the formula V = (B * r) / k.

Here's the step-by-step explanation:

1. The volume of a pyramid is given by the formula V = (1/3) * B * h, where B is the area of the base and h is the height.
2. In this case, the base of the pyramid is a square with area B, and the height is r.
3. So, the volume of one pyramid can be calculated as V = (1/3) * B * r.
4. Since the sphere is made up of k congruent small square-based pyramids, the volume of one pyramid is equal to the volume of the sphere divided by k.
5. Therefore, V = (1/3) * B * r = (B * r) / k.

So, the correct answer is V = (r * B) / k.