NCERT Solutions for Class 9 Maths Chapter 13- Surface areas and volumes

NCERT Solutions for Class 9 Maths Chapter 13 – Surface Areas and Volumes are given here in simple, step-by-step form. NCERT stands for the National Council of Educational Research and Training, the body that makes your textbook. This chapter deals with solid shapes, that is, three-dimensional objects like a box, a can, an ice-cream cone, a ball and a bowl. For each solid you learn two things: its surface area, which is the total area of its outer faces, and its volume, which is the space it takes up.

The chapter covers five solids in all: the cuboid and cube, the cylinder, the cone, the sphere and the hemisphere. For each one, you learn the curved surface area, the total surface area and the volume. Once the formulas are clear, the questions become simple substitution. This page gives you a short introduction to the whole chapter, all the important formulas in one place, and links to the full solutions for each exercise.

NCERT Solutions for Class 9 Maths Chapter 13- Surface areas and volumes

Exercises in This Chapter

Chapter 13 is divided into the following exercises. Click any link to open the full step-by-step solutions for that exercise.

All the Formulas of Chapter 13 in One Place

In the formulas below, l is length, b is breadth, h is height, r is radius and l (slant) is the slant height of a cone. The value of π is taken as 22/7 or 3.14 unless the question says otherwise.

Cuboid

  • Total surface area = 2(lb + bh + hl)
  • Lateral surface area (four walls) = 2h(l + b)
  • Volume = l × b × h
  • Length of the longest rod (diagonal) = √(l2 + b2 + h2)

Cube (side a)

  • Total surface area = 6a2
  • Lateral surface area = 4a2
  • Volume = a3
  • Diagonal = a√3

Right Circular Cylinder

  • Curved surface area = 2Ï€rh
  • Total surface area = 2Ï€r(r + h)
  • Volume = πr2h

Right Circular Cone

  • Slant height l = √(r2 + h2)
  • Curved surface area = πrl
  • Total surface area = πr(l + r)
  • Volume = 1/3 × Ï€r2h

Sphere (radius r)

  • Surface area = 4Ï€r2
  • Volume = 4/3 × Ï€r3

Hemisphere (radius r)

  • Curved surface area = 2Ï€r2
  • Total surface area = 3Ï€r2
  • Volume = 2/3 × Ï€r3

Simple Tips for This Chapter

  • Keep the units the same. Change everything to the same unit before you start. Surface area comes out in square units, and volume in cubic units.
  • Curved versus total. Curved surface area leaves out the flat top and bottom. Total surface area includes them. Read the question carefully to see which one is asked.
  • Choose the right value of Ï€. If the radius is a multiple of 7, using 22/7 makes the numbers cancel neatly. Otherwise 3.14 is fine.
  • Find the slant height first for a cone. Many cone questions give the radius and the height, so work out the slant height with √(r2 + h2) before finding the surface area.

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