Surface Areas and Volumes

Board: CBSE | Class: Class 9

Comprehensive study notes for Surface Areas and Volumes by Ajay Yadav (Math King of Katargam). Master every concept with clear explanations, solved examples, and practice problems.

Key Concepts

Cube

A cube has 6 equal square faces. Lateral Surface Area (LSA) = 4a². Total Surface Area (TSA) = 6a². Volume = a³ where a = edge length.

Cuboid

A cuboid has 6 rectangular faces. LSA = 2h(l+b). TSA = 2(lb + bh + hl). Volume = l × b × h.

Right Circular Cylinder

LSA (Curved Surface Area) = 2πrh. TSA = 2πr(r+h). Volume = πr²h.

Right Circular Cone

Slant height l = √r² + h². CSA = πrl. TSA = πr(r+l). Volume = (1/3)πr²h.

Sphere and Hemisphere

Sphere: CSA = TSA = 4πr². Volume = (4/3)πr³. Hemisphere: CSA = 2πr². TSA = 3πr². Volume = (2/3)πr³.

Important Formulas

Cube	TSA = 6a², V = a³
Cuboid	TSA = 2(lb+bh+hl), V = lbh
Cylinder	CSA = 2πrh, TSA = 2πr(r+h), V = πr²h
Cone	l = √r²+h², CSA = πrl, V = (1/3)πr²h
Sphere	CSA = TSA = 4πr², V = (4/3)πr³
Hemisphere	CSA = 2πr², TSA = 3πr², V = (2/3)πr³

Solved Examples

Example 1: Find the TSA and volume of a cube with edge 5 cm.

Solution: TSA = 6 × 5² = 150 cm². Volume = 5³ = 125 cm³.

Example 2: Find the volume of a cylinder with radius 7 cm and height 10 cm.

Solution: V = πr²h = (22/7) × 49 × 10 = 1540 cm³.

Example 3: Find the surface area of a sphere with radius 7 cm.

Solution: TSA = 4πr² = 4 × (22/7) × 49 = 616 cm².

Practice Questions

1. Find the LSA of a cuboid with dimensions 8 cm, 6 cm, 5 cm.
2. A cylindrical tank has radius 3.5 m and height 10 m. Find its capacity in litres.
3. Find the slant height of a cone with radius 6 cm and height 8 cm.
4. The volume of a sphere is 4851 cm³. Find its radius.
5. How many litres of water can a hemispherical bowl of radius 21 cm hold?

Download PDF

Click here to download the PDF notes for this chapter.

Video Lessons

Watch video explanations on our Videos page.