Today is rung 1 of 2 on this topic
Volume of cylinders, cones and spheres
Can do: Applies the volume formulas correctly and reasons about the relationships between them.
Why it matters
The cone-is-a-third-of-a-cylinder relationship is memorable when demonstrated and forgettable when memorised.
What it looks like when it's wobbly
Mixes up which formula has the third and which has the four-thirds, and uses diameter for radius.
⏱️ Two-minute check
"Cone radius 3, height 6 — volume? How does it compare to the cylinder with the same dimensions?"
Solid looks like: About 56.5, and exactly one third.
The full activity for this topic · 25 minutes
Pour It and See
- 1Make a cone and a cylinder with the same radius and height out of card.
- 2Fill the cone and pour it into the cylinder. Repeat. It takes exactly three.
- 3Now they'll never forget the third.
- 4Calculate a real one: the volume of a can, an ice cream cone, a ball.
- 5Work backwards: given a volume, find a missing radius.
If it's too hard
Cylinders only, from measurement.
If it's too easy
Composite solids, and comparing volumes when a dimension is doubled.
Say this
"Pour it again. How many cones filled the cylinder? That's your fraction — you never have to memorise it."