Volume
Lessons in this chapter
About Volume
Volume closes 8th grade with the volume formulas for three curved solids.
Volume of Cylinders and Cones introduces both formulas together specifically because they're related: a cone's volume is exactly one-third of a cylinder's volume, given the same base radius and height, the same 1-in-3 relationship 7th grade's Surface Area and Volume chapter demonstrated between prisms and pyramids.
Volume of Spheres introduces the sphere volume formula, (4/3)πr³, applying the same real-number and exponent skills from earlier in 8th grade to calculate with it.
Both lessons, Volume of Cylinders and Cones and Volume of Spheres, are 8th grade math worksheets worked inside the page. The questions use real measurements and are marked as they are answered, so forgetting the one third in the cone formula shows up immediately rather than at the end. Both are free to try, with no login needed for your first 3.
Frequently asked questions
Volume of Cylinders and Cones introduces both formulas together because they are related: a cone holds exactly one third of the cylinder that shares its base radius and height. Volume of Spheres then adds V = (4/3)πr³, which uses only the radius. Both lessons also ask your child to work backward from a known volume to a missing radius or height, drawing on the square and cube roots from earlier in the grade. This sits in the Common Core domain Geometry (8.G).
The volume of a cylinder is V = πr²h, where r is the radius of the circular base and h is the height: essentially the area of the circular base multiplied by how tall the cylinder is.
The volume of a cone is V = (1/3)πr²h: exactly one-third of a cylinder's volume with the same base radius and height, the same relationship 7th grade's Surface Area and Volume chapter showed between prisms and pyramids.
The volume of a sphere is V = (4/3)πr³, using only the radius, since a sphere is a single curved surface with no separate base or height.
Substitute the known volume and other known measurement into the formula, then solve for the missing variable. This often requires dividing, then taking a square root (for cylinders and cones) or cube root (for spheres) to isolate the radius.
Forgetting to multiply by one-third after calculating πr²h, since a cone is exactly one-third of the matching cylinder, skipping that final step gives the cylinder's volume instead of the cone's.