Cones, spheres and pyramids · Grade 8
In Grade 8 you learn: volume of cones, pyramids and spheres.
Pyramids, cones and spheres are solids that do not have the same cross-section all the way through. A pyramid or cone holds exactly one third of the prism or cylinder with the same base and height, and a sphere has its own formulas for volume and surface area.
Key facts
- Pyramid: V = ⅓ × base area × height.
- Slant height: l² = r² + h² (Pythagoras).
Worked examples
Example 1
Find the volume of a cone with radius 5 cm and height 12 cm, to 1 d.p.
Answer: 314.2 cm³
Example 2
A metal sphere of radius 6 cm is melted and made into spheres of radius 2 cm. How many small spheres are made?
Answer: 27