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Chapter Analysis
Intermediate21 pages • EnglishQuick Summary
Chapter 9 of Class 8 Mathematics, titled 'Mensuration', introduces students to concepts related to calculating the perimeter and area of various plane figures like quadrilaterals, and extends to finding the surface area and volume of solid shapes such as cubes, cuboids, and cylinders. It involves decomposing complex geometrical shapes into simpler ones to analyze their measurement properties. Problem-solving exercises based on these concepts are integral to the chapter, fostering a deeper understanding of spatial measurements through practical examples and exercises.
Key Topics
- •Perimeter and area calculations for quadrilaterals
- •Surface area of cubes, cuboids, and cylinders
- •Volume calculations for cubes, cuboids, and cylinders
- •Decomposing polygons to calculate area
- •Practical applications of mensuration in real-world contexts
- •Difference between lateral surface area and total surface area
Learning Objectives
- ✓Understand and apply formulas for perimeter and area of plane figures
- ✓Calculate surface area and volume of three-dimensional shapes
- ✓Analyze complex geometrical problems using decomposition
- ✓Foster problem-solving skills through real-life mensuration applications
- ✓Develop spatial awareness by arranging and visualizing volumetric objects
Questions in Chapter
The shape of the top surface of a table is a trapezium. Find its area if its parallel sides are 1 m and 1.2 m and perpendicular distance between them is 0.8 m.
Page 106
The diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.
Page 106
Given a cylindrical tank, in which situation will you find surface area and in which situation volume.
Answer: (a) To find how much it can hold. (b) Number of cement bags required to plaster it. (c) To find the number of smaller tanks that can be filled with water from it.
Page 119
Additional Practice Questions
Calculate the volume of a cylinder with a base radius of 5 cm and a height of 10 cm.
easyAnswer: Volume = π × radius² × height = 3.14 × 5² × 10 = 785 cm³.
A rectangular sheet with dimensions 20 cm by 30 cm is rolled to form a cylinder. What is the volume of the resulting cylinder?
mediumAnswer: By rolling the sheet along its width, the height of the cylinder is 20 cm, and the circumference becomes the base circumference 30 cm. The radius is thus 30/2π ≈ 4.77 cm. Volume = π × (4.77)² × 20 ≈ 1431.4 cm³.
Explain the concept of lateral surface area and calculate it for a box with dimensions 10 cm × 5 cm × 2 cm.
mediumAnswer: Lateral surface area refers to the sum of the areas of all the vertical faces (the sides) of a solid object. For this cuboid, LSA = 2h(l + b) = 2 × 2(cm) (10 cm + 5 cm) = 60 cm².
Design a hexagonal field using trapeziums, and calculate the total area given each side of the hexagon is 8 m.
hardAnswer: A hexagon can be divided into 6 equilateral triangles. Area of one triangle = (√3/4) × side² = (√3/4) × (8)² ≈ 27.71 m². Total area = 6 × 27.71 ≈ 166.26 m².
Mohan wishes to paint two opposite faces of a cubical container each with a side of 5 cm. Calculate the total area to be painted and the amount of paint required if 1 L covers 10 m².
easyAnswer: Area per face = 5 × 5 = 25 cm² = 0.0025 m². Total area for two faces = 0.005 m². Paint required = 0.005/10 = 0.0005 L.