Brand Logo
LoginDownload App
Search
Brand Logo

Edzy for Classes 6-12

Edzy is a personal AI tutor for CBSE and State Board students, with curriculum-aligned guidance, practice, revision, and study plans that adapt to each learner.

  • Email: always@edzy.ai
  • Phone: +91 96256 68472
  • WhatsApp: +91 96256 68472
  • Address: Sector 63, Gurgaon, Haryana

Follow Edzy

Browse by Class

  • CBSE Class 6
  • CBSE Class 7
  • CBSE Class 8
  • CBSE Class 9
  • CBSE Class 10
  • CBSE Class 11
  • CBSE Class 12
Explore the CBSE resource hub

Explore Edzy

  • Study Resources
  • Free Study Tools
  • Best Apps for Board Exams
  • Edzy vs ChatGPT
  • About Us
  • Why We Built Edzy
  • Blog
  • CBSE AI Tutor

Support & Legal

  • Help & FAQs
  • Accessibility
  • Privacy Policy
  • Terms & Conditions
  • Refund Policy
  • Cookie Policy
  • Site Directory

© 2026 Edzy. All rights reserved.

Curriculum-aligned learning paths for students in Classes 6-12.

Chapter Hub

SURFACE AREAS AND VOLUMES

This chapter focuses on calculating surface areas and volumes of three-dimensional shapes, specifically cones and spheres. The formulas and their derivations are provided through examples and activities.

Summary, practice, and revision
CBSE
Class 9
Mathematics
Mathematics

SURFACE AREAS AND VOLUMES

Chapter Summary

Playing 00:00 / 00:00

Download NCERT Chapter PDF for SURFACE AREAS AND VOLUMES – Latest Edition

Access Free NCERT PDFs & Study Material on Edzy – Official, Anytime, Anywhere

Live Challenge Mode

Ready to Duel?

Challenge friends on the same chapter, answer fast, and sharpen your concepts in a focused 1v1 battle.

NCERT-aligned questions
Perfect for friends and classmates

Why start now

Quick, competitive practice with instant momentum and zero setup.

More about chapter "SURFACE AREAS AND VOLUMES"

Chapter 11 delves into the concepts of surface areas and volumes, particularly for right circular cones and spheres. It begins by introducing the surface area of a right circular cone, derived through practical activities that help visualize the shape formation. Essential formulas such as the curved surface area (πrl) and the total surface area (πr(l + r)) are discussed alongside examples for better understanding. The chapter progresses to the sphere, explaining its surface area (4πr²) and volume (∼4/3πr³), reinforced by hands-on experiments that illustrate the relationship between sphere volume and water displacement. Exercises challenge students to apply their knowledge and calculations derived from these geometric principles.
Learn Better On The App
Built for collaborative learning

Study With Friends

Join classmates, challenge them in duels, and make practice more engaging.

Quick duels
Shared momentum

Faster access to practice, revision, and daily study flow.

Edzy mobile app preview

Surface Areas and Volumes - Class 9 Mathematics

Explore the concepts of surface areas and volumes in this Class 9 Mathematics chapter on cones and spheres. Understand formulas through examples and practical applications.

The formula for the curved surface area of a right circular cone is given by πrl, where r is the radius of the base and l is the slant height of the cone.
To find the total surface area of a cone, you use the formula πr(l + r), where r is the base radius and l is the slant height. This accounts for both the curved surface area and the area of the circular base.
The surface area of a sphere is calculated using the formula 4πr², where r represents the radius of the sphere.
The volume of a right circular cone is calculated using the formula V = (1/3)πr²h, where r is the base radius and h is the height of the cone.
The volume of a sphere is calculated using the formula V = (4/3)πr³, where r is the radius. This formula illustrates that the volume increases with the cube of the radius.
The volume of a cone can be derived by noting that a cone with the same base and height as a cylinder fills one-third of the cylinder's volume. Thus, V = (1/3)πr²h represents this relationship.
The main difference is that a cone has a single circular base and tapers to a point (the vertex), while a cylinder has two parallel circular bases and has uniform height. The volume and surface area formulas for their shapes reflect these differences.
The slant height (l) of a cone can be calculated using the Pythagorean theorem. If h is the height and r is the radius, then l = √(r² + h²).
One suggested activity involves filling a cone with sand and transferring it to a cylinder. This demonstrates how three cones of the same dimensions fill one cylinder, reinforcing the concept of volume.
Yes, a hemisphere's total surface area is calculated as 3πr², which includes both the curved surface area (2πr²) and the flat base area (πr²).
The volume of a sphere is directly related to the cube of its radius. This reveals that if the radius is doubled, the volume increases by a factor of eight.
Cones and spheres are commonly found in everyday objects like ice cream cones, traffic cones, and balls. Understanding their dimensions helps in practical design and manufacturing.
To find the radius given the surface area (S), rearrange the surface area formula: r = √(S/(4π)). This allows you to derive the radius directly from known surface data.
Common mistakes include using incorrect units, miscalculating dimensions, or confusing volume formulas between spheres and cones. It's essential to identify the shape correctly before applying formulas.
These formulas help in a variety of fields such as construction, manufacturing, and shipping, where accurate volume measurements are crucial for material efficiency and planning.
Increasing the radius increases the surface area and volume exponentially. For spheres, volume increases with the cube of radius, while for cones it is proportional to the square of radius multiplied by height.
Calculations assume perfect geometric shapes without irregularities, and that π is used with sufficient precision, often approximated as 3.14 or 22/7.
The volume of a container is directly representative of its capacity, allowing calculations to determine how much liquid or material can be held within it.
Cones and spheres are integral in architecture and design. Their structural and aesthetic properties enable efficient resource usage and elevate functionality in various applications.
Tools such as rulers for straight measurements, calipers for precision, and digital measuring devices can be helpful for accurate calculations of dimensions.
Hands-on activities, real-life applications, and interactive models can significantly help in reinforcing the understanding of surface areas and volumes of geometric shapes.
Understanding these shapes helps in practical applications across science, engineering, architecture, and many fields, ensuring that students are well-prepared for future challenges.

Chapters related to "SURFACE AREAS AND VOLUMES"

LINES AND ANGLES

This chapter covers the properties of angles formed by intersecting lines and parallel lines. Understanding these properties is essential for geometry and real-life applications such as architecture.

Start chapter

TRIANGLES

This chapter explains triangles, their properties, and the concept of congruence. Understanding triangles is essential in geometry as they form the basis for many other shapes and concepts.

Start chapter

QUADRILATERALS

This chapter covers the properties of quadrilaterals, particularly parallelograms. Understanding these concepts is crucial as they form the foundation for geometry and various real-world applications.

Start chapter

CIRCLES

This chapter introduces key concepts related to circles, including angles formed by chords and arcs, and the properties of cyclic quadrilaterals.

Start chapter

HERON’S FORMULA

This chapter explains Heron’s Formula, which allows you to find the area of a triangle using the lengths of its sides without needing the height.

Start chapter

STATISTICS

This chapter introduces graphical methods for representing data, emphasizing their importance for easier understanding and comparison.

Start chapter

SURFACE AREAS AND VOLUMES Summary, Important Questions & Solutions | All Subjects

Question Bank

Worksheet

Revision Guide

Formula Sheet