Maryland Math 7.GR.B.4.b
The Standard
- 7.GR.B.4
- Solve mathematical problems with and without context involving area, surface area, and volume of two- and three-dimensional objects.
Solve problems involving volume of curved-surface solids, including cones, cylinders, and spheres—figures without edges.
Maryland College and Career Ready Standards for Mathematics (2025) · REASON WITH AND ABOUT GEOMETRIC FORMULAS TO SOLVE PROBLEMS AND JUSTIFY SOLUTIONS IN CONTEXT.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the volume of cones, cylinders, and spheres in word problems. They use the radius, choose the right formula, and give answers in cubic units.
What Mastery Looks Like
- Given a sphere with a 6 cm diameter, a student uses a 3 cm radius and finds its volume as 36π cubic cm. They can also explain why a cone holds one third as much as a cylinder with the same base and height.
Common Misconceptions
- Students may use the diameter as the radius. They may forget to divide a cone’s volume by 3 or use a squared radius for a sphere. Some give square units instead of cubic units.
How to Assess It
- Exit ticket: A cylinder and cone each have a radius of 3 cm and height of 6 cm. A sphere has a radius of 3 cm. Find all three volumes and circle the largest.
Lesson moves
Ways to Teach It
Fill a cone with rice and pour it into a cylinder with the same base and height; count how many pours fill the cylinder.
Ask students to write why a cone and cylinder with the same radius and height cannot hold the same amount.
Give pairs cards with solid diagrams, dimensions, and volumes; have them match each diagram to its volume card.
Compare the volume of a 3 cm radius ball with a can of the same radius and 6 cm height.
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Printable 7.GR.B.4.b Worksheet
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