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Chapter Analysis
Intermediate10 pages • EnglishQuick Summary
The chapter 'Surface Areas and Volumes' teaches students about calculating the surface area and volume of various solid figures and combinations of solids. It introduces concepts like total surface area and curved surface area, and applies these to combinations such as cylinders with hemispheres or cones. The chapter includes real-life applications, helping students understand how these calculations can be used in practical contexts. The exercises and examples further reinforce the understanding of creating and solving problems involving composite solids.
Key Topics
- •Surface Area of Cuboid
- •Volume of Cylindrical Solids
- •Surface Area of a Combination of Solids
- •Volume Calculation of Composite Solids
- •Curved Surface Area
- •Total Surface Area
Learning Objectives
- ✓Calculate the surface area of basic solid shapes.
- ✓Understand how to find the volume of composite shapes.
- ✓Apply formulas to solve real-world geometry problems.
- ✓Develop skills to find the total and curved surface areas.
- ✓Relate the concepts to practical applications like cylindrical tanks or spherical balloons.
Questions in Chapter
1. Two cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
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2. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
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3. A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of the same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
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4. A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.
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5. A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
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6. A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.
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Additional Practice Questions
Calculate the surface area of a cylinder with a height of 10 cm and a base radius of 5 cm.
mediumAnswer: The curved surface area (CSA) is 2πrh, and the total surface area (TSA) is 2πr(h + r). Here, CSA = 2π(5)(10) = 100π cm². TSA = 2π(5)(10 + 5) = 150π cm².
A cone has a base diameter of 8 cm and a height of 12 cm. Find its volume.
easyAnswer: The volume of a cone is (1/3)πr²h. With r = 4 cm, h = 12 cm, the volume is (1/3)π(4)²(12) = 64π cm³.
What is the volume of a spherical balloon with a radius of 7 cm?
easyAnswer: The volume of the sphere is (4/3)πr³. Hence, the volume is (4/3)π(7)³ = 1436.75 cm³ approximately.
Find the total surface area of a cube with an edge length of 6 cm.
mediumAnswer: The total surface area of a cube is 6a². Thus, the area is 6(6)² = 216 cm².
A cylinder has a total height of 20 cm and a diameter of 10 cm. If it is partially filled with water to a height of 10 cm, what is the volume of the empty part?
mediumAnswer: The total volume is πr²h = π(5)²(20) = 500π cm³. The filled volume is π(5)²(10) = 250π cm³. So, the empty volume is 250π cm³.