AmbifulWorksheets

Cheat sheet
CBSE · Class 9 · Mathematics

Math of Space: Surface Area and Volume

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