Class 10 Maths - BIHAR
Surface Areas and Volumes
The Chapter 'Surface Areas and Volumes' in Class 10 Bihar Board (BSEB) mathematics builds upon your previous knowledge of basic geometric shapes by introducing combinations of solids. You will learn to calculate the total surface area and volume of objects formed by joining two or more basic shapes, such as a cone on a cylinder, a hemisphere with a cylinder, or frustum of a cone. This chapter is exceptionally important for the BSEB matriculation examination, frequently featuring in both short-answer and long-answer descriptive questions, testing your visualization and calculation skills.
Start Learning FreeKey Concepts
Surface Area of Combined Solids
The total surface area of a combined solid is the sum of the curved surface areas of each individual visible part, not simply the sum of their total surface areas.
Volume of Combined Solids
The volume of a solid formed by joining two basic shapes is simply the sum of the volumes of the individual constituent shapes.
Conversion of Solids
When a solid is converted from one shape to another, its total volume remains unchanged, which helps in finding unknown dimensions like height or radius.
Frustum of a Cone
When a right circular cone is cut by a plane parallel to its base, the lower portion remaining is called a frustum of a cone, having two circular bases of different radii.
Important Formulas
Board Exam Info
In the Bihar Board (BSEB) Class 10 Mathematics exam, this chapter typically carries around 6 to 10 marks. Questions usually include 1-2 objective (MCQ) questions, a short-answer 2-mark question, and a crucial 5-mark long-answer question involving combined shapes or conversion of solids.
Frequently Asked Questions
Do I need to add total surface areas when two solids are combined?
No, when two solids are joined together, you only calculate the curved surface areas of the exposed outer surfaces that are visible.
What happens to the volume when a solid is melted and recast into another shape?
The total volume remains exactly the same. You can set the volume of the original shape equal to the volume of the new shape to find missing dimensions.
How do I remember the slant height (l) formula for a cone or frustum?
For a cone, use Pythagoras theorem: l = square root of (r^2 + h^2). For a frustum, use l = square root of [h^2 + (r1 - r2)^2].
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