8.G.9: Volume of Cylinders, Cones and Spheres
Also written as 8.G.C.9 and CCSS.MATH.CONTENT.8.G.C.9 · Cluster: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
The Official Wording
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, Grade 8, Geometry · Read it at the source · Checked October 14, 2026
What 8.G.9 Means in Plain English
Eighth graders work out what round containers hold. A can is base area times height, V = πr²h, so radius 4 cm and height 10 cm gives 502.4 cm³ with 3.14 for π. A matching cone holds a third, and a sphere holds 4/3 πr³.
Real problems mix the three: how many cone scoops fill a cylinder tub, or how much empty space a ball leaves in its box. High school explains why the cylinder and cone formulas work, with Cavalieri’s principle (HSG-GMD.1), and applies them to composite solids (HSG-GMD.3).
8.G.9 I Can Statements
- I can find the volume of a cylinder from its radius and height.
- I can explain why a cone holds a third of its cylinder.
- I can find the volume of a sphere and use it in problems.
8.G.9 Worked Example
A cone and a scoop with the same radius, and the question every kid holding an ice cream cone has wondered about.
A scoop of ice cream is a sphere 6 cm across. It sits on a cone that is 6 cm across the top and 10 cm deep. If the scoop melts, will the cone hold it all? Use 3.14 for π.
- Both are 6 cm across, so both radii are half of that.r = 6 ÷ 2 = 3 cm
- Cone: one third of a cylinder with the same base and height.V = ⅓ × 3.14 × 3² × 10 = ⅓ × 3.14 × 90 = 94.2 cm³
- Sphere: four thirds times π times the radius cubed.V = 4/3 × 3.14 × 3³ = 4/3 × 3.14 × 27 = 113.04 cm³
- Compare the two volumes.113.04 − 94.2 = 18.84 cm³ more than the cone holds
Check it: Work in multiples of π first: the cone is ⅓ × 9 × 10 = 30π and the sphere is 4/3 × 27 = 36π. The difference is 6π, and 6 × 3.14 = 18.84.
Common Mistakes with 8.G.9
Using the diameter as the radius
Sphere 6 cm across: 4/3 × 3.14 × 6³ = 904.32 cm³
Try this: Circle the word across or diameter and halve the number before writing any formula. Every one of these formulas is built on the radius.
Forgetting the third in the cone
Cone: 3.14 × 3² × 10 = 282.6 cm³
Try this: Picture three full cones poured into a cylinder of the same base and height. It takes all three, so divide by 3.
Squaring when the sphere needs a cube
Sphere: 4/3 × 3.14 × 3² = 37.68 cm³
Try this: Check the units: volume is in cubic units, so the sphere formula needs three lengths multiplied, r³, not r².
Where 8.G.9 Fits
Practice 8.G.9
Quick Check
- A cylinder tank has a radius of 2 m and a height of 5 m. What is its volume? Use 3.14 for π.
- A cone and a cylinder have the same radius and height. The cylinder holds 600 mL. How much does the cone hold?
- A ball has a radius of 10 cm. What is its volume? Use 3.14 for π.