Pyramids, cones, spheres and composite solids
Pour a pyramid into its prism and a sphere into its cylinder to see where the 13 and the 23 come from. Open a cone into a sector, find its slant height with Pythagoras' theorem, and work out the volume and surface area of a tower.
- UK: Year 10
- France: grade 8
- Germany: grade 10
- Iran: grade 9
- Afghanistan: grade 8
- Syria: grade 8
- Palestine: grade 7
- Ukraine: grade 11
- Russia: grade 10
Guide
This studio follows GCSE geometry and measures (G17): the volume and surface area of pyramids, cones, spheres and composite solids. Iran teaches it in Year 9 and Afghanistan in Year 8. All lengths are in cm and π = 3.14.
In the pouring missions the pyramid or sphere fits exactly inside a prism or cylinder with the same base and height. Each tap on + pours one pyramid (or one sphere) of water into it, and your child sees how far the water rises.
Turn the solid by dragging it, with the arrow buttons or with the arrow keys. The line under the picture says what can be seen from where.
Common mistakes this studio works on: forgetting the 13 for pyramids and cones, mixing up the vertical height (for volume) and the slant height (for the curved surface), swapping 4πr2 and 43πr3, and counting the face where two parts of a composite solid are joined.