CCSS.Math.Content.8.G.C.9
The Standard
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Common Core State Standards for Mathematics · Geometry
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students identify whether a solid is a cylinder, cone, or sphere and select the matching volume formula. They substitute given measurements, calculate accurately, and solve for volume in context.
What Mastery Looks Like
- Students choose the correct formula, identify the needed measurements, and calculate exact or decimal volumes. They convert diameter to radius when needed and label answers with cubic units.
Common Misconceptions
- Students often use the diameter as the radius or use slant height instead of vertical height. They may omit the cone’s factor of one-third, confuse the sphere formula with surface area, or write square units instead of cubic units.
How to Assess It
- Give students a cylinder with radius 3 cm and height 8 cm, a cone with the same dimensions, and a sphere with radius 3 cm. Ask for each volume in terms of pi and with correct units.
Lesson moves
Ways to Teach It
Fill a cone with rice and pour it into a matching cylinder, then record how many cone fills complete the cylinder.
Ask students to explain why doubling a sphere’s radius increases its volume by more than two times.
Run a card sort matching diagrams, dimensions, volume formulas, and calculated answers for cylinders, cones, and spheres.
Compare the capacities of cylindrical cans and cone-shaped cups using package measurements and estimated volumes.
Free download
Printable 8.G.C.9 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.8.G.C.9, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetBefore This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.6.EE.A.2c
Volume problems require substituting dimensions into formulas and evaluating powers and products in the correct order.
- CCSS.Math.Content.7.G.B.4
Circle area and radius work carry into cylinder and cone volume formulas, especially using πr² as the base area.
- CCSS.Math.Content.6.G.A.2
Rectangular prism volume develops volume units, fractional dimensions, and formula use that support applying cylinder, cone, and sphere formulas.
What This Unlocks
Mastery here sets students up for these next.
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Related Standards
- CCSS.Math.Content.8.G.C
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
- CCSS.Math.Content.7.G.B
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
- CCSS.Math.Content.6.G.A
Solve real-world and mathematical problems involving area, surface area, and volume.
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