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SURFACE AREA AND VOLUME CLASS 10 ICSE
1. The ratio between the curved surface area and the total surface area of a right circular cylinder is 1:3. Find the ratio between the height and radius of the cylinder.
Hence, the required ratio between height and radius of the cylinder is 1 : 2.
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2. A cylindrical roller 2.5 m in length, 1.75 m in radius when rolled on a road was found to cover an area of 5500m². How many revolutions did it make?
Hence, the number of revolution made by the roller is 200.
3. The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. Find the
(i) radius of the cylinder.(ii) volume of cylinder.
Sol. Given, circumference of base of a cylindrical vessel = 132 cm and height = 25 cm
(i) We know that base of a cylinder is in the shape of a circle.
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4. In a cylinder, if radius is halved and height is doubled, then find its volume.
Sol. Let height of cylinder = h
and radius of base of cylinder = r
5. The cost of painting the outer curved surface of a cylinder at ₹1.50 per cm² is ₹660. If the height of the cylinder is 2 m. Then, find the area of base of cylinder.
Sol. Given, height of the cylinder = 2 m = 200 cm
[ 1 m = 100 cm]
Total cost of painting = ₹ 600
and rate of painting the outer curved surface area of the cylinder = ₹ 1.50 per cm2
660 = Curved surface area
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6. A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.
Sol. Given, radius of a cone, r = 7 cm
And height of a cone h = 24 cm
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7. A conical tent is 10 m high and the radius of its base is 24 m. Find
(i) the slant height of the tent.
(ii) the cost of the canvas required to make the tent, if the cost of 1m2 canvas is ₹70.
(iii) the volume of air contained in the conical tent.
Sol. Given, height of a conical tent, h = 10 m
and radius, r = 24 m
8. A solid cone of radius 5 cm and height 7 cm is given. Calculate
(i) the curved surface area of a cone.
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9. The volume of a conical tent is 1232 m³ and the area of the base floor is 154 m². Calculate
(i) radius of the floor.
(ii) height of the tent.
(iii) length of the canvas required to cover this conical tent, if its width is 2 m.
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10. Monika has a piece of canvas, whose area is 551 m². She uses it to made conical tent with a base radius of 7 m. Assuming that all the stitching margins and the wastage incurred while cutting, amounts to approximately 1 m², then find the volume of the tent that can be made with it.
Sol. Let l m be the slant height and h m be the height of cone.
Here, base radius of cone = 7 m.
Total area of canvas = 551 m2 and wastage = 1 m2
= (551 – 1)m2 = 550 m2
12. A wooden toy is in the shape of a cone mounted on a cylinder, as shown in the following figure. If the height of the cone is 24 cm, the total height of the toy is 60 cm and the radius of the base of the cone is equal to twice the radius of the base of the cylinder is 10 cm, then find the total surface area of the toy.
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Sol. Given, height of cylinder, h = Total height of toy – Height of cone
= 60 – 24 = 36 cm
Radius of cone, r = 10 cm.
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ALSO VISIT:
10th ICSE
| Also Learn: | Attempt theQuiz on Mathematics : | Attempt theQuiz on Physics: | Attempt theQuiz on Biology: | Attempt theQuiz on Chemistry: |
| 1.Surface Areas and Volumes 2. ELECTRICITY 3. METALS AND NON METALS 4. ATOMS AND MOLECULES 5. GST6. PHOTOSYNTHESIS IN HIGHER PLANTS 7. ABSORPTION BY ROOTS 8. QUADRATIC EQUATIONS 9. LINEAR INEQUATIONS 10. RECURRING DEPOSIT 11. CIRCULAR MOTION 12. MCQ WORK POWER ENERGY 13. ACIDS BASES AND SALTS 14. MCQ ON ACIDS BASES AND SALTS 15. ROTATIONAL MOTION MASS 2 16. ROTATIONAL MOTION MASS 1 17. MCQ ON PERIODIC TABLE 2 18. MCQ ON PERIODIC TABLE 1 19. CELL CYCLE AND CELL DIVISION 20.REFLECTION CLASS 10 ICSE NOTES 21.EQUATION OF LINE CLASS 10 ICSE NOTES 22.CIRCLE CLASS 10 ICSE NOTES | QUIZ ON SURFACE AREAS AND VOLUMES- MATHEMATICS QUIZ ON SECTION AND MID-POINT | QUIZ ON ELECTRICITY- PHYSICS | QUIZ 1 ON METALS AND NON-METALS – CHEMISTRY QUIZ 2 ON METALS AND NON-METALS – CHEMISTRY |