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Chapter Analysis
Intermediate14 pages • EnglishQuick Summary
This chapter focuses on surface area and volume calculations for various geometric shapes, including cones, spheres, and hemispheres. It covers both the derivation and applications of formulas such as the surface area of cones and spheres and the volume of cones and spheres. Practical activities are included to help students understand these concepts better. The chapter concludes with exercises to reinforce learning.
Key Topics
- •Surface Area of Cones
- •Surface Area of Spheres
- •Surface Area of Hemispheres
- •Volume of Cones
- •Volume of Spheres
- •Volume of Hemispheres
Learning Objectives
- ✓Understand the concept of surface area and volume in geometric figures.
- ✓Learn to apply formulas to calculate the surface area and volume of cones, spheres, and hemispheres.
- ✓Enhance problem-solving skills through practical exercises.
- ✓Explore real-life applications of geometric concepts.
- ✓Visualize the relationship between different geometric shapes.
Questions in Chapter
Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.
Page 141
Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.
Page 141
Curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find (i) radius of the base and (ii) total surface area of the cone.
Page 141
Find the volume of the right circular cone with (i) radius 6 cm, height 7 cm (ii) radius 3.5 cm, height 12 cm.
Page 147
Find the capacity in litres of a conical vessel with (i) radius 7 cm, slant height 25 cm (ii) height 12 cm, slant height 13 cm.
Page 147
A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.
Page 148
A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.
Page 148
Additional Practice Questions
Calculate the volume of a cone with a base radius of 5 m and a height of 12 m.
mediumAnswer: The volume of the cone is 314.16 m³, calculated using the formula V = (1/3)πr²h.
If the surface area of a sphere is 154 cm², what is its radius?
mediumAnswer: The radius of the sphere is 3.5 cm, derived from the surface area formula 4πr² = 154.
What is the total surface area of a hemisphere with a radius of 10 cm?
mediumAnswer: The total surface area is 942 cm², using the formula 3πr².
A cylindrical container has a sphere of radius 7 cm snugly fit inside. Calculate the surface area of the cylinder if its height equals the diameter of the sphere.
hardAnswer: The surface area of the cylinder is 615.75 cm².
A conical tank is filled with water up to a height of 5 meters. Calculate the volume of water if the radius of the base is 3 meters.
mediumAnswer: The volume of water in the tank is 47.1 m³.