Volume of Prisms, Cylinders, Cones and Spheres

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Mathematics · Geometry
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Page 2
Volume of Prisms, Cylinders, Cones and
Spheres
Mathematics · Geometry · Grades 9-10 · 50 minutes
Time needed
50 minutes (one class period)
Prep
Copy the 2-page worksheet (one per student). Write the volume formulas on the board.
Technology
None. A basic calculator is optional.
Student
independence
High. Students work alone with a calculator if available.
Copies to make
One 2-page worksheet per student
Materials
Pencils, Worksheet, Whiteboard or chalkboard, Calculators (optional)
Goal for today: Students will select and apply the correct volume formula for prisms, cylinders, cones and spheres,
including a combined solid.
Before the bell
☐ Copy the worksheet, one per student (2 pages).
☐ Write on the board: Prism or cylinder V = B × h (B = area of the base). Cone V = ⅓ × B × h. Sphere V =
(4/3)πr³. Volume is measured in cubic units.
☐ Keep the answer key on your desk. You do not need to solve anything yourself.
Say this to start
Good morning! Today’s geometry practice is on volume, which is how much space is inside a 3-D shape. The formulas
are on the board. The worksheet describes each solid in words, so students are encouraged to sketch what they see.
They may leave answers with π or round to the nearest hundredth.
Run of show
Minutes
What you do
What students do
0–5
Take attendance. Hand out the worksheet face down.
Settle in and take out a pencil.
5–12
Read the formulas from the board aloud. Then read this
example: a cylinder with radius 2 and height 5 has volume
π(2²)(5) = 20π cubic units.
Follow along.
12–18
Tell students to match shapes to formulas (Part A,
questions 1–4).
Match each solid to its formula.
18–40
Tell students to work Part B (questions 5–12) in the work
boxes. Say that no pictures are given; students should
sketch each solid. Walk the room.
Sketch, write the formula, substitute, and
solve.
40–46
Tell students to finish questions 13–15.
Compare cone and cylinder volumes and
answer the multiple-choice question.
46–50
Read the answers aloud from the key while students check.
Collect all worksheets.
Check their work and hand in the
worksheet.


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Mathematics · Geometry
SP-GEOM-008  ·  Free to print and use in your classroom  ·  substituteplans.com
Page 3
If things go wrong
• If a student confuses radius and diameter, remind them that the radius is half the diameter. Several problems
give a radius directly.
• If students forget the ⅓ in the cone formula, point to the board and say a cone holds one third of what a
matching cylinder holds.
• If students’ answers seem too large, ask if the units are cubic.
• If the class is noisy, remind them this is independent work.
Early finishers
• Find the volume of a cube with side 7, then the volume of the largest sphere that fits inside it. Compare them.
• Explain in your own words why a cone holds exactly one third of a matching cylinder.
• Create your own cylinder problem and trade with a neighbor.
Support and challenge
• Support: Allow calculators and have students complete questions 1–5, 7 and 8 only.
• Challenge: Ask students to find the radius of a sphere with a volume of 36π (answer: 3).
Notes for the teacher (you fill this in)
Jot a few lines before you leave. A full Daily Sub Report is in the free Sub Survival Kit at SubstitutePlans.com.
How far the class got / what to pick up next:
Students who were especially helpful:
Anything the teacher should know: