Volume of prisms and cylinders

Learning Objectives Define volume and identify the base and height of various prisms and cylinders. State and apply the general formula for the volume of a right prism (V = B * h). State and apply the specific formula for the volume of a cylinder (V = π * r^2 * h). Calculate the volume of composite solids composed of prisms and cylinders. Solve problems to find a missing dimension (e.g., height, radius) of a prism or cylinder given its volume. Apply volume formulas to solve real-world application problems. Ever wonder how much soda fits in a can or how much water is needed to fill a swimming pool? 🏊‍♀️ That's all about calculating volume! Volume measures the amount of three-dimensional space an object occupies. In this tutorial, you will master the single, powerful fo...

TermDefinitionExample VolumeThe amount of three-dimensional space an object occupies, measured in cubic units (like cm³, m³, or in³).A cube with side lengths of 1 cm has a volume of 1 cubic centimeter (1 cm³). PrismA three-dimensional solid with two identical, parallel polygon faces called bases. The other faces are rectangles that connect the corresponding sides of the bases.A standard cardboard box is a rectangular prism. A Toblerone box is a triangular prism. CylinderA three-dimensional solid with two identical, parallel circular bases and one curved lateral surface connecting them.A can of soup or a roll of paper towels. Base (of a Prism or Cylinder)One of the two parallel, congruent faces that define the shape. The shape of the base gives the prism its name (e.g., a triangular base m...

General Formula for Volume of Prisms and Cylinders V = B \cdot h This is the fundamental formula. The Volume (V) of any right prism or cylinder is found by multiplying the Area of its Base (B) by its perpendicular height (h). Volume of a Rectangular Prism V = l \cdot w \cdot h This is a specific version of the general formula where the base is a rectangle. The base area (B) is calculated as length (l) times width (w). Volume of a Cylinder V = \pi r^2 h This is a specific version of the general formula where the base is a circle. The base area (B) is calculated as pi (π) times the radius (r) squared.