Grade 8 · Geometry · MAT-08-GEO-011
Find Volume of Cylinders
Represent and solve find volume of cylinders problems using precise mathematical notation, multiple representations, and justified reasoning.
Learning objectives
What you should be able to do
- Represent and solve find volume of cylinders problems using precise mathematical notation, multiple representations, and justified reasoning.
- Interpret and verify find volume of cylinders results in context, including units, constraints, and reasonableness.
Prerequisite check
Make sure the foundation is ready.
Grade 8 uses this prerequisite as active knowledge in a more formal representation.
Learn
Build the idea from meaning, not memorization.
Meaning and structure
Find Volume of Cylinders belongs to geometry. Identify the governing property or relationship before choosing a procedure.
Multiple representations
Represent find volume of cylinders numerically and symbolically, then connect it to the Grade 8 Math Box. Tables, graphs, equations, coordinate models, diagrams, and verbal descriptions must agree.
Verification and interpretation
Check with substitution, an inverse operation, an equivalent representation, geometric invariants, estimation, or context. State whether the result is exact or approximate and preserve relevant units and constraints.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Solid Volume Lab
- Model find volume of cylinders in the Math Box.
- Change one input and predict which quantities or invariants should change.
- Explain what the visual, equation, and numerical result say about the same relationship.
Worked examples
Twenty different ways to see the concept work.
Find exact volume of a cylinder with r=2, h=3.
V = 12πCylinder volume is πr²h.
Find exact volume of a cylinder with r=3, h=4.
V = 36πCylinder volume is πr²h.
Find exact volume of a cylinder with r=4, h=5.
V = 80πCylinder volume is πr²h.
Find exact volume of a cylinder with r=5, h=6.
V = 150πCylinder volume is πr²h.
Find exact volume of a cylinder with r=6, h=7.
V = 252πCylinder volume is πr²h.
Find exact volume of a cylinder with r=7, h=8.
V = 392πCylinder volume is πr²h.
Find exact volume of a cylinder with r=8, h=9.
V = 576πCylinder volume is πr²h.
Find exact volume of a cylinder with r=9, h=10.
V = 810πCylinder volume is πr²h.
Find exact volume of a cylinder with r=2, h=11.
V = 44πCylinder volume is πr²h.
Find exact volume of a cylinder with r=3, h=12.
V = 108πCylinder volume is πr²h.
Find exact volume of a cylinder with r=4, h=13.
V = 208πCylinder volume is πr²h.
Find exact volume of a cylinder with r=5, h=14.
V = 350πCylinder volume is πr²h.
Find exact volume of a cylinder with r=6, h=15.
V = 540πCylinder volume is πr²h.
Find exact volume of a cylinder with r=7, h=16.
V = 784πCylinder volume is πr²h.
Find exact volume of a cylinder with r=8, h=17.
V = 1088πCylinder volume is πr²h.
Find exact volume of a cylinder with r=9, h=18.
V = 1458πCylinder volume is πr²h.
Find exact volume of a cylinder with r=2, h=19.
V = 76πCylinder volume is πr²h.
Find exact volume of a cylinder with r=3, h=20.
V = 180πCylinder volume is πr²h.
Find exact volume of a cylinder with r=4, h=21.
V = 336πCylinder volume is πr²h.
Find exact volume of a cylinder with r=5, h=22.
V = 550πCylinder volume is πr²h.
Practice
Guided practice with hints
01Find exact volume of a cylinder with r=6, h=23.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: V = 828π
02Find exact volume of a cylinder with r=7, h=24.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: V = 1176π
03Find exact volume of a cylinder with r=8, h=25.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: V = 1600π
04Find exact volume of a cylinder with r=9, h=26.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: V = 2106π
05Find exact volume of a cylinder with r=2, h=27.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: V = 108π
06Find exact volume of a cylinder with r=3, h=28.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: V = 252π
Practice
Independent practice
01Find exact volume of a cylinder with r=4, h=29.
Answer: V = 464π
02Find exact volume of a cylinder with r=5, h=30.
Answer: V = 750π
03Find exact volume of a cylinder with r=6, h=31.
Answer: V = 1116π
04Find exact volume of a cylinder with r=7, h=32.
Answer: V = 1568π
05Find exact volume of a cylinder with r=8, h=33.
Answer: V = 2112π
06Find exact volume of a cylinder with r=9, h=34.
Answer: V = 2754π
07Find exact volume of a cylinder with r=2, h=35.
Answer: V = 140π
08Find exact volume of a cylinder with r=3, h=36.
Answer: V = 324π
Common mistakes
Learn to catch the error, not just the answer.
Rigid transformations preserve size; dilations generally do not.
a²+b²=c² applies to right triangles.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Use transformations in design and coordinate geometry and Pythagorean reasoning for distance.
- Model capacities of cylindrical, conical, and spherical objects.
Challenge problems
Find exact volume of a cylinder with r=4, h=37.
V = 592π
Find exact volume of a cylinder with r=5, h=38.
V = 950π
Find exact volume of a cylinder with r=6, h=39.
V = 1404π
Find exact volume of a cylinder with r=7, h=40.
V = 1960π
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 8 Algebra & Modeling Sprint
Solve find volume of cylinders problems and justify each result with a valid verification method.
Practice
Mastery check
01Find exact volume of a cylinder with r=8, h=41.
Answer: V = 2624π
02Find exact volume of a cylinder with r=9, h=42.
Answer: V = 3402π
03Find exact volume of a cylinder with r=2, h=43.
Answer: V = 172π
04Find exact volume of a cylinder with r=3, h=44.
Answer: V = 396π
05Find exact volume of a cylinder with r=4, h=45.
Answer: V = 720π
06Find exact volume of a cylinder with r=5, h=46.
Answer: V = 1150π
07Find exact volume of a cylinder with r=6, h=47.
Answer: V = 1692π
08Find exact volume of a cylinder with r=7, h=48.
Answer: V = 2352π
Terminology
Words to know
- transformation
- A rule mapping a figure to an image.
- congruent
- Having the same size and shape.
- similar
- Having equal corresponding angles and proportional corresponding lengths.
- Pythagorean theorem
- For a right triangle, a²+b²=c².
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Grade 8 instructional guidance, mathematical practices, modeling, and progression toward high-school mathematics.Common Core State Standards for Mathematics — Grade 8
Grade-level expectations for real numbers, equations, functions, geometry, and statistics.Principles to Actions: Ensuring Mathematical Success for All
Research-informed emphasis on reasoning, representations, discourse, productive struggle, and conceptual understanding.