NY Next Generation Math NY-8.G.9
The Standard
Given the formulas for the volume of cones, cylinders, and spheres, solve mathematical and real-world problems.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use provided formulas to solve volume problems involving cones, cylinders, and spheres. They substitute dimensions, compute accurately, and interpret units in mathematical or real contexts.
What Mastery Looks Like
- The student selects the correct provided formula and distinguishes radius, diameter, and height. The student reports exact answers in terms of pi or reasonable approximations with cubic units.
Common Misconceptions
- Students may use diameter in place of radius or forget to square the radius. They may omit the one-third factor for cones or use square units.
How to Assess It
- Provide all three volume formulas. Ask students to find the volumes of a cylinder and cone with radius 3 and height 8, then compare them.
Lesson moves
Ways to Teach It
Fill a cone with rice three times and pour it into a matching cylinder to examine the one-third relationship.
Ask students how changing only the radius affects each provided volume formula.
Play Solid Formula Match with dimensions, diagrams, and volume expressions.
Estimate the capacity of a cylindrical can or spherical container using measured dimensions and a provided formula.
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Printable NY-8.G.9 Worksheet
A ready-to-print activity worksheet aligned to NY-8.G.9, with an answer key for the teacher on its own page. No account needed.
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