Volume Solids
1. Let's start by stating the formulas for the volume of each solid.
2. Volume of a pyramid: The volume $V$ of a pyramid with base area $B$ and height $h$ is given by
$$V = \frac{1}{3}Bh$$
This means you multiply the base area by the height and then divide by 3.
3. Volume of a sphere: The volume $V$ of a sphere with radius $r$ is
$$V = \frac{4}{3}\pi r^3$$
This formula comes from calculus and represents the space inside the sphere.
4. Volume of a cylinder: The volume $V$ of a cylinder with base radius $r$ and height $h$ is
$$V = \pi r^2 h$$
You find the area of the circular base $\pi r^2$ and multiply by the height.
5. To summarize:
- Pyramid: $V = \frac{1}{3}Bh$
- Sphere: $V = \frac{4}{3}\pi r^3$
- Cylinder: $V = \pi r^2 h$
These formulas allow you to calculate the volume of these solids when you know the necessary dimensions.