Objective: To solve statement problems involving volumes of 3-D solids Volume Problems

KEY To Solving Volume Problems To solve volume problems, it is helpful to: draw and label a diagram write necessary formulas

Example: Irregular Solid A pharmacist is filling medicine capsules.  The capsules are cylinders with half spheres on each end.  If the length of the cylinder is 12 mm and the radius is 2 mm, how many cubic mm of medication can one capsule hold?  (Round answer to the nearest tenth of a cubic mm.)

Example: Irregular Solid 12 mm NOTE: r = 2 mm 4 mm Volume (cylinder) + Volume (sphere)* V = _____ V = V = _____ V = _____ V= __________ V = _____ V = _____ BH Π r2 H Π (2mm)2 (12mm) 48 Π mm3

Example: Irregular Solid Find the volume in cubic feet. 7’  25’ 18 ’ V (∆ prism) = _____ + V (□ prism) = _____

Example: Irregular Solid Total Volume = 1,575 ft.3 + 4,050 ft.3 = 5,625 ft. 3 Example: Irregular Solid Find the volume in cubic feet. V (∆ prism) = _____ + V (□prism) = _____ 1,575 ft. 3 4,050 ft. 3 V (∆ prism) = _____ + V (□prism) = _____

ALERT! If you know the volume of a solid, you can calculate an unknown length of a base or the solid’s height. EXAMPLE A The volume of a triangular prism is 1440 cm3. The base is a right triangle with legs 8 and 15 cm in length. Find the height of the prism. V (prism/cylinder) = ____________ _____________ = _____________

ALERT! If you know the volume of a solid, you can calculate an unknown length of a base or the solid’s height. EXAMPLE B The volume of a cylinder is 2816 m3. Find the radius of the base of the cylinder if it has a height of 14 m. Use 22/7 for . V (prism/cylinder) = _____________ V (prism/cylinder) = _____________ _____________ = _____________ _____________ = _____________ _____________ = _____________ _____________ = _____________ _____________ = _____________

Final Checks for Understanding Meg A Byte’s queen-size waterbed is 7 ft. long, 5 ft. wide, and 8 inches thick. Find the bed’s volume to the nearest cubic foot. If 1 cubic foot of water weights 62.4 pounds, what is the weight of the water in Meg’s bed to the nearest pound?

HOMEWORK ASSIGNMENT: VOLUME PROBLEMS WS