Chapter 12 Surface Areas and Volumes Exercise-01
EXERCISE 12.1
Unless stated otherwise, take
1. 2 cubes each of volume
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Solution2. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is
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Solution
It can be observed that radius
Height of hemispherical part
Height of cylindrical part
Inner surface area of the vessel = CSA of cylindrical part + CSA of hemispherical part
Inner surface area of vessel
3. A toy is in the form of a cone of radius
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Solution
It can be observed that the radius of the conical part and the hemispherical part is same (i.e.,
Height of hemispherical part
Height of conical part
Slant height
Total surface area of toy
4. A cubical block of side
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Solution
From the figure, it can be observed that the greatest diameter possible for such hemisphere is equal to the cube’s edge, i.e.,
Radius
Total surface area of solid = Surface area of cubical part + CSA of hemispherical part
- Area of base of hemispherical part
Total surface area of solid
5. A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter
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Solution
Diameter of hemisphere
Radius of hemisphere
Total surface area of solid = Surface area of cubical part + CSA of hemispherical part
- Area of base of hemispherical part
Total surface area of solid
6. A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see Fig. 12.10). The length of the entire capsule is
Fig. 12.10
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Solution
It can be observed that
Radius
part
Length of cylindrical part
Surface area of capsule
7. A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are
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Solution
Given that,
Height
Diameter of the cylindrical part
Radius of the cylindrical part
Slant height
Area of canvas used
Cost of
Cost of
Therefore, it will cost Rs 22000 for making such a tent.
8. From a solid cylinder whose height is
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Solution
Given that,
Height
Diameter of the cylindrical part
Therefore, radius
Slant height
Total surface area of the remaining solid will be
The total surface area of the remaining solid to the nearest
9. A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in Fig. 12.11. If the height of the cylinder is
Fig. 12.11
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Solution
Radius
Height of cylindrical part
Surface area of article