Class 10 Maths - CBSE
Surface Areas and Volumes
The Chapter 'Surface Areas and Volumes' in Class 10 Mathematics builds upon previous classes by exploring complex three-dimensional shapes. Students learn to calculate the total surface area, curved surface area, and volume of combined solids such as toys, tents, and vessels. This chapter is vital for CBSE board exams because it tests spatial visualization and multi-step calculation skills. Questions often involve converting one solid shape into another or finding dimensions of composite figures, making it a high-scoring yet application-heavy section that frequently features in 3-mark and 4-mark subjective questions.
Start Learning FreeKey Concepts
Surface Area of Combined Solids
When two or more basic solids are joined together, the total surface area is the sum of the visible curved surface areas of the individual parts, not their total surface areas.
Volume of Combined Solids
The total volume of a solid formed by joining two or more basic shapes is simply the sum of the volumes of each individual component.
Conversion of Solids
When a solid is melted and reshaped into a new solid, the total volume remains constant, which is the key principle used to solve conversion problems.
Frustum of a Cone
When a right circular cone is cut by a plane parallel to its base, the lower part is called a frustum, which has two circular bases of different radii.
Important Formulas
Board Exam Info
In the CBSE Class 10 Mathematics board exam, this chapter typically carries around 5 to 6 marks. Questions usually appear as long-answer problems (3 or 4 marks) involving real-life scenarios like tents, capsules, or metallic toys, where two shapes are combined or a solid is melted and recast.
Frequently Asked Questions
Do I add the total surface areas when two solids are joined?
No, you only add the curved or visible surface areas. Internal touching surfaces are not counted in the total surface area.
How do I know whether to use surface area or volume in a word problem?
Use volume if the object is melted, recast, filled with a liquid, or contains material. Use surface area if you are painting, wrapping, or covering the outer boundary of the object.
Is it mandatory to substitute the value of pi as 22/7?
Unless specified otherwise in the question, you can leave your answer in terms of pi or use 22/7 or 3.14 as instructed.
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