Subjects geometry

Volume Solids

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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.