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Class 9 Math of Space: Surface Area and Volume: cheat sheet
CBSE Mathematics. Surface areas and volumes of cones, spheres and hemispheres, with π = 22/7 unless told otherwise.
Key ideas
- The slant height l of a cone joins the tip to a point on the edge of the base.
- Curved surface area leaves out the flat base; total surface area includes it.
- A hemisphere has a curved surface 2πr² and a flat circle πr² on top.
- A cone has a third of the volume of a cylinder with the same base and height.
- 1000 cm³ = 1 litre and 1 m³ = 1000 litres.
- Choose r so that it cancels with 7 when π = 22/7 makes the arithmetic easy.
Remember
| Cone | l = √(r² + h²); CSA = πrl; TSA = πr(l + r); V = ⅓πr²h |
| Sphere | SA = 4πr²; V = (4/3)πr³ |
| Hemisphere | CSA = 2πr²; TSA = 3πr²; V = (2/3)πr³ |
| Units | 1 litre = 1000 cm³ |
Watch out
- Using the height h where the slant height l is needed.
- Using the diameter for the radius.
- Forgetting the flat top when asked for the total surface area of a hemisphere.
Worked example
A hemispherical bowl has an inner radius of 84 cm. How many litres of juice can it hold (π = 22/7)?
Working: (2/3) × 22/7 × 84³ = 1,241,856 cm³ = 1241.856 litres
Answer: 1241.856 litres
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