In this lesson:
By the end of this lesson, you should be able to:
A can and a funnel have circular bases. A basketball has none. So how can base times height work?
A sphere fills exactly two-thirds of the cylinder that just encloses it (height ).
Doubling multiplies the volume by 8, since .
A marble has radius 1.5 cm:
A water balloon has diameter 20 cm. First .
A sphere has volume in³. Find .
For : — not .
The sphere uses (volume), not (area). Units are cubic.
A basketball has diameter 24 cm. Find its volume.
Halve the diameter, then cube. Leave your answer in terms of .
You now know three formulas. Real problems describe objects, not shapes.
How do you decide which formula to use?
Can, pipe, tank → cylinder. Funnel, party hat → cone. Ball, globe → sphere.
Cone (, ) plus hemisphere (): .
A grain silo: cylinder (, ) plus a cone roof (, ).
A cylindrical mug (, ) versus a cone cup (, ).
Compute both volumes and compare. Try it before advancing.
A spherical balloon has volume cm³. Find its radius.
Set up and solve. No template — work it all the way.
Use , not — the sphere is three-dimensional Cubing means , not
✓ Cylinder is the baseline; cone is one-third of it ✓ Sphere stands apart: and , and fills two-thirds of its cylinder Read the shape clues; cube don't square; halve the diameter
Next: in high school, Cavalieri's principle proves these formulas.
Click to begin the narrated lesson
Know the formulas for the volumes of cones, cylinders, and spheres