Class 10 Maths - MP
Surface Areas and Volumes
The chapter 'Surface Areas and Volumes' in Class 10 Mathematics builds upon your foundational knowledge of 2D shapes to explore 3D objects. You will learn how to calculate the total surface area, curved surface area, and volume of combined solids such as cylinders, cones, spheres, hemispheres, and frustums of cones. This chapter is highly scoring and plays a vital role in the Madhya Pradesh Board (MPBSE) examinations. Understanding these concepts helps in solving practical real-life problems like finding the capacity of containers, material required for manufacturing objects, and conversion of one solid shape into another.
Start Learning FreeKey Concepts
Cuboid and Cube
Solid figures bounded by six rectangular or square faces, where total surface area, lateral surface area, and volume depend on length, breadth, and height.
Cylinder and Cone
A cylinder has two parallel circular bases and a curved surface, while a circular cone tapers smoothly from a flat circular base to a point called the apex.
Sphere and Hemisphere
A sphere is a perfectly round geometrical 3D object, and a hemisphere is exactly half of a sphere divided by a plane passing through its center.
Frustum of a Cone
When a right circular cone is cut by a plane parallel to its base, the lower portion remaining is called the frustum of a cone.
Combination of Solids
Real-life objects are often combinations of two or more basic shapes, such as a tent being a cylinder surmounted by a cone.
Important Formulas
Board Exam Info
In the MPBSE Class 10 Mathematics board examination, 'Surface Areas and Volumes' typically carries around 6 to 8 marks. Questions usually include 1-mark objective questions, 2-mark short answer questions, and a major 4-mark long answer question involving combination of solids or conversion of solid shapes from one form to another.
Frequently Asked Questions
How do I know whether to find surface area or volume in a word problem?
Find the surface area when the problem asks for the amount of material used, cost of painting, wrapping, or covering. Find the volume when it asks for the capacity of a container, the amount of liquid it can hold, or when a solid is melted and recast into another shape.
What is the slant height of a cone and how is it calculated?
The slant height (l) is the distance from the outer edge of the base to the apex along the curved surface. It is calculated using Pythagoras theorem: l = sqrt(r^2 + h^2), where r is the radius and h is the height.
When two solids are combined, do we add their surface areas?
No, when two solids are joined together, the total surface area of the new combined figure is the sum of the curved surface areas visible from the outside. The touching faces are internal and are not included in the total surface area.
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