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

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

3. 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.)

4. 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

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

6. 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) = _____

7. 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) = ____________
_____________ = _____________

8. 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) = _____________ _____________ = _____________ _____________ = _____________ _____________ = _____________ _____________ = _____________ _____________ = _____________

9. 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?

10. HOMEWORK ASSIGNMENT:
VOLUME PROBLEMS WS