8.7.A
The Standard
solve problems involving the volume of cylinders, cones, and spheres
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students identify the solid, choose the matching volume formula, and use the given radius, diameter, and height correctly. They solve for volume in exact or decimal form and include cubic units.
What Mastery Looks Like
- Students select the correct formula, substitute measurements accurately, and solve with or without a calculator. They give exact answers in terms of pi or decimal estimates and use cubic units.
Common Misconceptions
- Students often use diameter as the radius or forget to square the radius. They may omit the cone's one-third factor, confuse sphere and cylinder formulas, or label volume with square units.
How to Assess It
- Give an exit ticket: A cone has radius 4 cm and height 9 cm. Find its exact volume and a decimal approximation, then label the units.
Lesson moves
Ways to Teach It
Fill a cone-shaped cup with rice three times to compare its capacity with a cylinder having the same base and height.
Ask students to explain why doubling a cylinder's radius changes its volume more than doubling its height.
Run a formula card sort, then have pairs solve cylinder, cone, and sphere task cards for points.
Compare packaging by calculating the capacities of a soup can, an ice cream cone, and a spherical ornament.
Keep exploring
Related Standards
- K.6.B
identify three-dimensional solids, including cylinders, cones, spheres, and cubes, in the real world
- 8.7.B
use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rec...
- 8.6.B
model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas
- 7.9.A
solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids
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