Compare and convert metric units of volume

Learning Objectives Use the Pythagorean theorem and trigonometric ratios to find unknown dimensions in 3D figures like cones and pyramids. Calculate the volume of cones, pyramids, and prisms using formulas that rely on dimensions derived from right triangles. Convert calculated volumes between cubic meters (m³), cubic centimeters (cm³), and cubic millimeters (mm³). Convert between units of solid volume (cm³) and units of capacity (milliliters and liters). Solve multi-step word problems that require calculating the volume of a 3D figure and converting the result to a different metric unit. Compare the volumes of different 3D figures by converting them to a common metric unit. Ever wondered how much water a conical party hat could hold if it were a cup? 🥳 Let's use the r...

TermDefinitionExample VolumeThe amount of three-dimensional space an object occupies, measured in cubic units like cubic meters (m³) or cubic centimeters (cm³).A cube with side lengths of 10 cm has a volume of 10 cm × 10 cm × 10 cm = 1000 cm³. CapacityThe amount a container can hold, typically used for fluids and measured in units like liters (L) or milliliters (mL).A standard water bottle has a capacity of 500 mL. Right Circular ConeA 3D figure with a circular base and a vertex. The height (h), radius (r), and slant height (l) form a right triangle, with the slant height as the hypotenuse.A traffic cone is a real-world example. If its height is 70 cm and its radius is 20 cm, these form the two legs of a right triangle inside the cone. Cubic Centimeter (cm³)A unit of volume equal to a cub...

Volume Conversion: Cubic Units 1 m³ = (100 cm)³ = 1,000,000 cm³ 1 cm³ = (10 mm)³ = 1,000 mm³ When converting between cubic units, you must cube the linear conversion factor. To go from a larger unit to a smaller unit, multiply. To go from a smaller unit to a larger unit, divide. Volume-Capacity Bridge 1 cm³ = 1 mL 1000 cm³ = 1 L 1 m³ = 1000 L This is the critical link between the volume of a solid object and the amount of fluid it can hold. Use this to switch between cubic measurements and capacity measurements. Volume of a Cone V = (1/3) * \pi * r^2 * h Calculates the volume of a cone. The perpendicular height (h) is often found using the Pythagorean theorem (r² + h² = l²) if the slant height (l) is given instead.