CCSS.Math.Content.HSG-GMD.A.3
The Standard
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students identify the solid, determine which measurements are given, and choose the matching volume formula. They substitute values, calculate accurately, and report answers in cubic units.
What Mastery Looks Like
- Students select the correct formula from a diagram or word problem and substitute the given measurements accurately. They calculate exact or approximate volume and label answers with cubic units.
Common Misconceptions
- Students often use diameter as radius or use slant height instead of perpendicular height. They may omit the one-third factor for cones and pyramids, or confuse surface area with volume.
How to Assess It
- Exit ticket: A cone has radius 3 cm and height 8 cm. Find its volume in exact form and to the nearest tenth.
Lesson moves
Ways to Teach It
Measure a can, paper cone, box pyramid, and ball, then calculate each volume and compare results with water or rice.
Ask students to explain why a cone and cylinder with equal bases and heights do not have equal volumes.
Run a card match with solid diagrams, dimensions, formulas, and calculated volumes.
Calculate the capacity of a grain silo, party hat, pyramid-shaped package, or spherical water tank using provided dimensions.
Free download
Printable HSG-GMD.A.3 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSG-GMD.A.3, 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 worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.7.G.B.4
Circle area and radius relationships carry into cylinder and cone volume formulas, especially using πr² as the base area.
- CCSS.Math.Content.8.G.C.9
Using cylinder, cone, and sphere volume formulas in grade 8 directly carries into high school problem solving, with pyramids added.
- CCSS.Math.Content.HSN-Q.A.1
Choosing and interpreting units in formulas carries over to using volume formulas correctly and reporting answers in cubic units.
Keep exploring
Related Standards
- CCSS.Math.Content.8.G.C
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
- CCSS.Math.Content.HSG-GMD.A.1
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.
- CCSS.Math.Content.HSG-GMD.A
Explain volume formulas and use them to solve problems
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