R
Rishtaara
Mathematics · Class 9

Surface Areas and Volumes

Surface areas and volumes of cubes, cuboids, cylinders, cones, and spheres.

3 sections15–25 min read6 MCQs · 2 examples

Chapter Overview

Surface Areas and Volumes in Class 9 covers formulas for cuboid, cube, right circular cylinder, cone, sphere, and hemisphere — total surface area, curved surface area, and volume.

Surface Areas

Cuboid TSA

2(lb + bh + hl)

Cube TSA

6a²

Cylinder CSA

2πrh

Cone CSA

πrl

Sphere SA

4πr²

Volumes

Cuboid

V = lbh

Cube

V = a³

Cylinder

V = πr²h

Cone

V = (1/3)πr²h

Sphere

V = (4/3)πr³

Solved Examples

Step-by-step solutions — read each step before checking the final answer.

Example 1: Cylinder volume

Find volume of cylinder with r = 7 cm, h = 10 cm.

  1. 1V = πr²h = π × 49 × 10
  2. 2V = 490π cm³ ≈ 1539.4 cm³

Answer

490π cm³

Example 2: Cube surface area

Edge of cube is 5 cm. Find total surface area.

  1. 1TSA = 6a² = 6 × 25

Answer

150 cm²

Key Points to Remember

  • CSA excludes top and bottom for solids like cylinder
  • Cone volume is ⅓ of cylinder with same base and height
  • Use consistent units (cm, m)

Exam Tips

  • Write formula before substituting
  • Use π = 22/7 or 3.14 as instructed
  • Distinguish TSA from CSA in word problems

Practice MCQs — Surface Areas and Volumes

Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.

Question 1 of 6Score: 0/0

Volume of cube of edge a is: