Volume

Learning Objectives Define volume and identify appropriate cubic units. Calculate the volume of rectangular prisms using the formula V = lwh. Calculate the volume of triangular prisms using the general prism formula V = Bh. Calculate the volume of composite figures made from prisms. Solve real-world problems involving the volume of prisms. Distinguish between volume and surface area of three-dimensional objects. Ever wondered how much water a swimming pool holds? 🏊‍♀️ Or how much space is inside a moving box? 📦 In this lesson, you'll learn how to measure the amount of space inside three-dimensional objects, known as volume. Understanding volume helps us solve practical problems in everyday life, from packing and construction to understanding how much liquid a contain...

TermDefinitionExample VolumeThe amount of three-dimensional space an object occupies or contains. It is measured in cubic units.The volume of a juice box tells you how much juice it can hold, typically measured in cubic centimeters (cm³) or milliliters (mL). Three-Dimensional (3D) FigureA geometric shape that has length, width, and height (or depth). These objects occupy space.A cube, a rectangular prism (like a brick), a cylinder (like a can), or a triangular prism are all 3D figures. PrismA 3D figure with two identical, parallel bases (polygons) and rectangular faces connecting them.A cereal box is a rectangular prism. A tent can be a triangular prism. Base (of a Prism)One of the two identical, parallel polygonal faces of a prism. The shape of the base defines the type of prism (e.g., r...

Volume of a Rectangular Prism $V = l \times w \times h$ To find the volume of a rectangular prism, multiply its length (l), width (w), and height (h). This is a specific case of the general prism formula where the base area (B) is $l \times w$. Volume of a General Prism $V = B \times h$ To find the volume of any prism, multiply the area of its base (B) by its height (h). The 'B' represents the area of the polygonal base, not just a single dimension. Volume of a Triangular Prism $V = (\frac{1}{2} \times b_{triangle} \times h_{triangle}) \times H_{prism}$ To find the volume of a triangular prism, first calculate the area of its triangular base ($B = \frac{1}{2} \times b_{triangle} \times h_{triangle}$), then multiply that base area by the height of the prism...