Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for 8th grade volume of cylinders cones and spheres? Then this Grade 8 lesson on Round Solids: Cylinder, Cone, Sphere Volume explains each idea step by step, with worked examples.
Quick answer: A cylinder holds πr²h, where r is the radius of its circular end and h its height. A cone holds one third as much as the matching cylinder, and a sphere holds (4/3)πr³. Always use the radius, halving any diameter first, and write the answer in cubic units, with π or with 3.14.
Standards: 8.G.C.9 · Level: Grade 8
How much can a cylinder hold?
Picture a tall stack of identical flat coins. Every coin covers a circle, and the stack is h units high, so the capacity equals the area of the circular end multiplied by the height.
V = πr2h
Use the radius of the circular end, not the distance across it.
What about a cone?
Fill a cone with sand and tip it into a can that has the same opening and the same depth. It takes three trips to fill the can, so a cone is a third of its matching cylinder.
V = 13πr2h
Measure h straight down from the tip to the middle of the base. The slanted edge is longer and is not used.
Where does the sphere formula come from?
Archimedes noticed that a ball snugly wrapped in a can, as wide and as tall as the ball, takes up exactly two thirds of the can. Take two thirds of what that can holds and the sphere formula appears.
V = 43πr3
Half a ball, called a hemisphere, holds half of this amount.
What steps solve a volume problem?
- Name the solid and write its formula.
- Convert a diameter into a radius by halving it.
- Substitute, cube or square the radius, and multiply.
- Keep π as a symbol for an exact result, or use 3.14 for a decimal.
- Finish with cubic units.
A soup can is 8 cm across and 11 cm tall. Half of 8 is 4, so the can holds π times 16 times 11, which is 176π cm3. Replacing π with 3.14 gives about 552.64 cm3.
Putting the diameter into the formula where the radius belongs makes a cylinder four times too big. Read the given measurement twice before squaring it.
With a cone or a sphere, multiply the whole numbers first, for example 4 · 27 = 108, and divide by 3 as the last step.
- Cylinder: V = πr2h.
- Cone: one third of the cylinder that matches its opening and height.
- Sphere: V = (4/3)πr3; a hemisphere holds half of that.
- The radius is half of the diameter, and every formula needs it.
- Capacity is measured in cubic units such as cm3 or ft3.
Round Solids: Cylinder, Cone, Sphere Volume: frequently asked questions
Why is a cone one third of a cylinder?
If a cone and a cylinder have the same base and height, three cones of liquid fill the cylinder exactly. This can be shown by pouring, and it gives the factor 1/3 in the cone formula.
Do I use the radius or the diameter in the formulas?
Always use the radius. If a problem gives the diameter, divide it by 2 first. Using the diameter by mistake makes a cylinder volume four times too large.
What does leaving the answer in terms of π mean?
It means writing π as a symbol, such as 160π cm3, instead of multiplying by 3.14. This is the exact value. Use 3.14 when a problem asks for a decimal approximation.
How do I find the volume of a hemisphere?
A hemisphere is half a sphere, so its volume is (2/3)πr3. For a radius of 5 inches, the volume is (2/3)π · 125 = (250/3)π cubic inches.
How can I find a missing height or radius?
Write the formula with the known volume, substitute the other measurement, and solve. For a cylinder with V = 225π and r = 5, 25πh = 225π gives h = 9.
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