CBSE Class 10 Maths Chapter 12: Surface Areas and Volumes NCERT Solutions

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NCERT Solutions PDF Class 10 PDF

This section provides NCERT Solutions for Class 10 Maths Chapter 12, focusing on Surface Areas and Volumes. It covers multiple-choice questions that explore how common objects are combinations of basic geometric shapes like cones, cylinders, spheres, and hemispheres. Students will learn to identify these composite shapes and understand the principles behind their construction. These solutions are designed to clarify concepts and aid in exam preparation by reinforcing the understanding of solid geometry. These solutions are particularly useful for students preparing for their board examinations. By working through these examples, students can build a strong foundation in identifying and analyzing composite solids, which is a key topic in the Class 10 Mathematics syllabus. The clear explanations and step-by-step reasoning help in grasping the fundamental concepts of surface areas and volumes of combined shapes, ensuring students are well-prepared to tackle similar problems in their exams.

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Quick info

BoardCBSE
ClassClass 10
SubjectMaths (Exemplar)
Session2026
LanguageEnglish
TypeNCERT Solutions
Chapter12. Surface Areas and Volumes

Chapter summary

This chapter focuses on understanding and identifying composite solids formed by combining basic geometric shapes. The NCERT Solutions for Chapter 12, Surface Areas and Volumes, cover multiple-choice questions that require students to recognize combinations of shapes like cones, cylinders, spheres, and hemispheres in everyday objects. It emphasizes the visual and conceptual understanding of how these shapes fit together to form more complex structures.

Learning outcomes

  • Identify composite solids formed by combining basic geometric shapes.
  • Recognize common objects as combinations of cones, cylinders, and spheres.
  • Understand the geometrical principles behind composite shapes.
  • Apply knowledge of basic shapes to analyze complex forms.

Topics covered

Paper topics

  • Surface Areas and Volumes
  • Composite Solids
  • Combinations of Geometric Shapes
  • Cone
  • Cylinder
  • Sphere
  • Hemisphere
  • Geometric Solid Identification

Important topics

  • Identifying composite solids
  • Recognizing shapes in everyday objects
  • Understanding combinations of cones and cylinders
  • Understanding combinations of spheres and cylinders
  • Understanding combinations of hemispheres and cones

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Questions and Solutions

Question 1

A cylindrical pencil sharpened at one edge is the combination of:
  1. a cone and a cylinder
  2. frustum of a cone and a cylinder
  3. a hemisphere and a cylinder
  4. two cylinders.
Solution: The correct option is (a) a cone and a cylinder.

A sharpened pencil consists of two parts: the main body, which is cylindrical, and the sharpened tip, which forms a cone. Therefore, the entire sharpened pencil can be viewed as a composite solid formed by joining a cone and a cylinder at their bases.

Question 2

A surahi is the combination of:
  1. a sphere and a cylinder
  2. a hemisphere and a cylinder
  3. two hemispheres
  4. a cylinder and a cone.
Solution: The correct option is (a) a sphere and a cylinder.

A typical surahi has a rounded, spherical bottom part for holding water and a narrower, cylindrical neck for pouring. Thus, it is a composite solid formed by a sphere and a cylinder attached at their surfaces.

Question 3

A plumbline (sahul) is the combination of:
  1. a cone and a cylinder
  2. a hemisphere and a cone
  3. frustum of a cone and a cylinder
  4. sphere and cylinder
Solution: The correct option is (b) a hemisphere and a cone.

A plumbline consists of a string attached to a weight. The weight is typically shaped with a hemispherical top and a conical bottom, which helps it hang vertically and provide a stable reference line. Therefore, it is a combination of a hemisphere and a cone.

Common mistakes

  • Incorrectly identifying the constituent shapes in a composite solid.
  • Confusing the properties of different geometric solids.
  • Misinterpreting the combination of shapes in real-world objects.

Revision tips

  • Visualize everyday objects and try to break them down into basic geometric shapes.
  • Pay close attention to the diagrams provided with the questions.
  • Review the definitions and formulas for cones, cylinders, and spheres.
  • Practice identifying combinations of solids in different contexts.

Practice MCQs

Q1. A sharpened pencil, when considered as a geometric solid, is primarily a combination of which two shapes?

Q2. A 'surahi', a traditional Indian water pitcher, is typically composed of which geometric solids?

Q3. A plumbline, used in construction, consists of which two geometric shapes?

Frequently asked questions

What is the main focus of CBSE Class 10 Maths Chapter 12 NCERT Solutions?

The main focus is on understanding and identifying composite solids, which are formed by combining basic geometric shapes like cones, cylinders, and spheres. It helps students recognize these combinations in real-world objects.

How do these solutions help in exam preparation?

These solutions clarify the concepts of composite solids by explaining how everyday objects are combinations of basic shapes. This understanding is crucial for solving problems related to surface areas and volumes of such combined figures in exams.

What geometric shapes are commonly combined in this chapter?

This chapter commonly deals with combinations of cones, cylinders, spheres, and hemispheres.

What is the shape of a sharpened pencil according to the solutions?

A sharpened pencil is described as a combination of a cone (the sharpened tip) and a cylinder (the main body).

How is a 'surahi' represented geometrically?

A 'surahi' is represented as a combination of a sphere (the bottom part) and a cylinder (the neck).

What shapes form a plumbline?

A plumbline is shown to be a combination of a hemisphere (the upper part) and a cone (the lower, weighted part).

Important links

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