Study Maharashtra Board Class 10 Maths 2 Chapter 7 Mensuration with important formulas and step-by-step explanations. This guide covers surface area, volume, combined solids, conversion of solids, frustum calculations, Practice Sets 7.1 to 7.4 and Problem Set 7.
Select the required practice set to study its concepts, formulas and solution methods.
Mensuration is the branch of mathematics that deals with measurements of geometrical figures. In this chapter, students calculate curved surface area, total surface area and volume of different three-dimensional solids.
A solid may be a cylinder, cone, sphere or hemisphere. Some practical objects are formed by joining two or more solids. For example, a toy may consist of a cone placed on a hemisphere, while a capsule may be formed using a cylinder and two hemispheres.
Students also learn problems involving the conversion of one solid into another. When a metallic sphere is melted and recast into smaller cones or cylinders, the volume of the material remains unchanged. Therefore, the volume before conversion equals the total volume after conversion.
Calculate curved and total surface areas by identifying the exposed surfaces of the solid.
Calculate the space occupied by cylinders, cones, spheres, hemispheres and combined solids.
Divide a complex object into familiar solids and add or subtract their areas and volumes correctly.
For a cone, slant height l can be calculated using l² = r² + h². Read the question carefully to decide whether the base is exposed. An attached circular surface should not be counted in the external surface area.
Practice Set 7.1 revises the basic formulas for cylinders, cones, spheres and hemispheres. Questions may ask for the curved surface area, total surface area, volume, radius, height or slant height.
Write the appropriate formula first and substitute all measurements using the same unit. If diameter is given, divide it by two to find the radius. When the slant height of a cone is not given, calculate it using the Pythagoras theorem before finding the curved surface area.
Practice Set 7.2 deals with combined solids. A single object may be formed by joining a cylinder and hemisphere, cone and hemisphere, or other familiar solids.
Draw a rough diagram and separate the object into basic solids. For volume, add the volumes of the joined parts. For surface area, count only the surfaces visible from the outside. The common circular surface at the joint is internal and should not be added.
Practice Set 7.3 includes conversion and recasting problems. When an object is melted and reshaped, no material is assumed to be lost. Therefore, the volume of the original solid is equal to the total volume of the new solid or solids.
If the question asks for the number of smaller objects formed, divide the volume of the original solid by the volume of one new object. Keep the value of π common on both sides whenever possible so the calculation becomes shorter and clearer.
Practice Set 7.4 covers advanced applications such as frustums and practical mensuration problems. A frustum is obtained when the top of a cone is cut by a plane parallel to its base.
Identify the larger radius, smaller radius, vertical height and slant height carefully. Do not interchange the two radii while substituting values. Some questions may also be solved by treating the frustum as the difference between a large cone and a smaller similar cone.
Problem Set 7 provides complete revision of the Mensuration chapter. It combines direct formula questions, combined solids, conversion of solids, capacity, volume, surface area and frustum applications.
Read the wording carefully to decide whether the question asks for area, volume, capacity, cost or the number of objects. Convert all measurements to the same unit before calculating. For capacity, remember that 1 litre equals 1000 cubic centimetres.
These Maharashtra Board Class 10 Maths 2 Chapter 7 Mensuration solutions cover Practice Sets 7.1, 7.2, 7.3 and 7.4 along with Problem Set 7. Follow every formula and unit conversion carefully, particularly in combined-solid and recasting questions.
Select any question to view its answer.
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