Cones, spheres and pyramids · Grade 10
In Grade 10 you learn: frustums and composite solids.
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.
- Cone: V = ⅓πr²h; curved surface area = πrl, where l is the slant height.
- Slant height: l² = r² + h² (Pythagoras).
- Sphere: V = 4/3 πr³; surface area = 4πr².
- Hemisphere: half a sphere; its total surface area is 2πr² + πr² = 3πr².
Worked examples
Example 1
The same cone (r = 5 cm, h = 12 cm): find its curved surface area, to 1 d.p.
Answer: 204.2 cm²