{"id":15784,"date":"2024-02-14T16:37:37","date_gmt":"2024-02-14T11:07:37","guid":{"rendered":"https:\/\/icsesolutions.com\/?p=15784"},"modified":"2024-02-15T15:17:40","modified_gmt":"2024-02-15T09:47:40","slug":"selina-icse-solutions-class-10-maths-cylinder-cone-sphere-surface-area-volume","status":"publish","type":"post","link":"https:\/\/icsesolutions.com\/selina-icse-solutions-class-10-maths-cylinder-cone-sphere-surface-area-volume\/","title":{"rendered":"Selina Concise Mathematics Class 10 ICSE Solutions Cylinder, Cone and Sphere"},"content":{"rendered":"
Selina Publishers Concise Mathematics Class 10 ICSE Solutions Chapter 20\u00a0Cylinder, Cone and Sphere (Surface Area and Volume)<\/strong><\/p>\n Question 1. Question 2.<\/strong><\/span> Question 4.<\/strong><\/span> Question 5.<\/strong><\/span> Question 6.<\/strong><\/span> Question 7.<\/span><\/strong> Question 8.<\/strong><\/span> Question 9.<\/strong><\/span> Question 10.<\/strong><\/span> Question 11.<\/strong><\/span> Question 12. Question 13. Question 14. Question 15. Question 16. Question 17. Question 18. Question 19. Question 20. Question 21. Question 22. Question 23. Question 24. Question 25.<\/strong><\/span> Question 26.<\/strong><\/span> Question 27. Question 28. Question 1.<\/strong><\/span> Question 2.<\/strong><\/span> Question 3.<\/strong><\/span> Question 4.<\/strong><\/span> Question 5.<\/strong><\/span> Question 6.<\/strong><\/span> Question 7.<\/strong><\/span> Question 8.<\/strong><\/span> Question 9.<\/strong><\/span> Question 10.<\/strong><\/span> Question 11.<\/strong><\/span> Question 12.<\/strong><\/span> Question 13.<\/strong><\/span> Question 14.<\/strong><\/span> Question 1.<\/strong><\/span> Question 2.<\/strong><\/span> Question 3.<\/strong><\/span> Question 4.<\/strong><\/span> Question 5.<\/strong><\/span> Question 6.<\/strong><\/span>Cylinder, Cone and Sphere Surface Area and Volume Exercise 20A –\u00a0Selina Concise Mathematics Class 10 ICSE Solutions<\/h3>\n
\n<\/strong><\/span>The height of a circular cylinder is 20 cm and the radius of its base is 7 cm. Find :
\n(i) the volume
\n(ii) the total surface area.
\nSolution:
\n<\/strong><\/span><\/p>\n
\nThe inner radius of a pipe is 2.1 cm. How much water can 12 m of this pipe hold?
\nSolution:<\/strong><\/span>
\n
\nQuestion 3.<\/strong><\/span>
\n
\nSolution:<\/strong><\/span>
\n<\/p>\n
\nHow many cubic meters of earth must be dug out to make a well 28 m deep and 2.8 m in diameter? Also, find the cost of plastering its inner surface at Rs 4.50 per sq meter.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\nWhat length of solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of external diameter 20 cm, 0.25 cm thick and 15 cm long?
\nSolution:<\/strong><\/span>
\n<\/p>\n
\nA cylinder has a diameter of 20 cm. The area of curved surface is 100 sq cm. Find:
\n(i) the height of the cylinder correct to one decimal place.
\n(ii) the volume of the cylinder correct to one decimal place.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\nA metal pipe has a bore (inner diameter) of 5 cm. The pipe is 5 mm thick all round. Find the weight, in kilogram, of 2 metres of the pipe if 1 cm3 of the metal weights 7.7 g.
\nSolution:<\/span><\/strong>
\nInner radius of the pipe = r =\\(\\frac{5}{2}\\) = 2.5 cm
\nExternal radius of the pipe = R = Inner radius of the pipe + Thickness of the pipe
\n= 2.5 cm + 0.5 cm
\n= 3 cm
\nLength of the pipe = h = 2 m= 200 cm
\nVolume of the pipe = External Volume – Internal Volume
\n
\nSince 1cm3<\/sup> of the metal weights 7.7 9,
\n\u2234 Weight of the pipe = (1728.6 \u00d7 7.7)g = \\(\\left(\\frac{1728.6 \\times 7.7}{1000}\\right)\\) kg = 13.31 kg<\/p>\n
\nA cylindrical container with diameter of base 42 cm contains sufficient water to submerge a rectangular solid of iron with dimensions 22 cm x 14 cm 10.5 cm. Find the rise in level of the water when the solid is submerged.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\nA cylindrical container with internal radius of its base 10 cm, contains water up to a height of 7 cm. Find the area of wetted surface of the cylinder.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\nFind the total surface area of an open pipe of length 50 cm, external diameter 20 cm and internal diameter 6 cm.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\n
\nSolution:<\/strong><\/span>
\n<\/p>\n
\n<\/strong><\/span>The radius of a solid right circular cylinder increases by 20% and its height decreases by 20%. Find the percentage change in its volume.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\n<\/strong><\/span>The radius of a solid right circular cylinder decreases by 20% and its height increases by 10%. Find the percentage change in its :
\n(i) volume
\n(ii) curved surface area
\nSolution:<\/strong><\/span>
\n
\n<\/p>\n
\n<\/strong><\/span>Find the minimum length in cm and correct to nearest whole number of the thin metal sheet required to make a hollow and closed cylindrical box of diameter 20 cm and height 35 cm. Given that the width of the metal sheet is 1 m. Also, find the cost of the sheet at the rate of Rs. 56 per m.
\nFind the area of metal sheet required, if 10% of it is wasted in cutting, overlapping, etc.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\n<\/strong><\/span>3080 cm3 of water is required to fill a cylindrical vessel completely and 2310 cm3<\/sup>\u00a0of water is required to fill it\u00a0upto\u00a05 cm below the top. Find :
\n(i)\u00a0radius\u00a0of the vessel.
\n(ii)\u00a0height\u00a0of the vessel.
\n(iii)\u00a0wetted\u00a0surface area of the vessel when it is half-filled with water.
\nSolution:<\/strong><\/span>
\n
\n<\/p>\n
\n<\/strong><\/span>Find the volume of the largest cylinder formed when a rectangular piece of paper 44 cm by 33 cm is rolled along it :
\n(i)\u00a0shorter\u00a0side.
\n(ii)\u00a0longer\u00a0side.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\n<\/strong><\/span>A metal cube of side 11 cm is completely submerged in water contained in a cylindrical vessel with diameter 28 cm. Find the rise in the level of water.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\n<\/strong><\/span>A circular tank of diameter 2 m is dug and the earth removed is spread uniformly all around the tank to form an embankment 2 m in width and 1.6 m in height. Find the depth of the circular tank.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\n<\/strong><\/span>The sum of the inner and the outer curved surfaces of a hollow metallic cylinder is 1056 cm2<\/sup>\u00a0and the volume of material in it is 1056 cm3<\/sup>. Find its internal and external radii. Given that the height of the cylinder is 21 cm.
\nSolution:<\/strong><\/span>
\n
\n<\/p>\n
\n<\/strong><\/span>The difference between the outer curved surface area and the inner curved surface area of a hollow cylinder is 352 cm2<\/sup>. If its height is 28 cm and the volume of material in it is 704 cm3<\/sup>;find its external curved surface area.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\n<\/strong><\/span>The sum of the heights and the radius of a solid cylinder is 35 cm and its total surface area is 3080 cm2<\/sup>, find the volume of the cylinder.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\n<\/strong><\/span>The total surface area of a solid cylinder is 616 cm2<\/sup>. If the ratio between its curved surface area and total surface area is\u00a01 :<\/span>\u00a02; find the volume of the cylinder.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\n<\/strong><\/span>A cylindrical vessel of height 24 cm and diameter 40 cm is full of water. Find the exact number of small cylindrical bottles, each of height 10 cm and diameter 8 cm, which can be filled with this water.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\n<\/strong><\/span>Two solid cylinders, one with diameter 60 cm and height 30 cm and the other with radius 30 cm and height 60 cm, are\u00a0metled<\/span>\u00a0and\u00a0recasted<\/span>\u00a0into a third solid cylinder of height 10 cm. Find the diameter of the cylinder formed.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\nSolution:<\/strong><\/span>
\n
\n<\/p>\n
\n
\nThe given figure shows a solid formed of a solid cube of side 40cm and a solid cylinder of radius 20 cm and height 50 cm attached to the cube as shown.
\nFind the volume and the total surface area of the whole solid (Take \u03c0 = 3.14)
\nSolution:<\/strong><\/span>
\n<\/p>\n
\n<\/strong><\/span>Two right circular solid cylinders have radii in the ratio 3 : 5 and heights in the ratio 2 : 3, Find the ratio between their :
\n(i)\u00a0curved\u00a0surface areas.
\n(ii)\u00a0volumes.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\n<\/strong><\/span>A dosed cylindrical tank, made of thin ironsheet, has diameter = 8.4 m and height 5.4 m. How much metal sheet, to the nearest m2<\/sup>, is used in making this tank, if \\(\\frac{1}{15}\\) of the sheet actually used was wasted in making the tank?
\n<\/span>Solution:<\/strong><\/span>
\n<\/p>\nCylinder, Cone and Sphere Surface Area and Volume Exercise 20B –\u00a0Selina Concise Mathematics Class 10 ICSE Solutions<\/h3>\n
\nFind the volume of a cone whose slant height is 17 cm and radius of base is 8 cm.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\n
\nSolution:<\/strong><\/span>
\n<\/p>\n
\nThe circumference of the base of a 12 m high conical tent is 66 m. Find the volume of the air contained in it.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\nThe radius and height of a right circular cone are in the ratio 5:12 and its volume is 2512 cubic cm. Find the radius and slant height of the cone. (Take \u03c0 = 3.14)
\nSolution:<\/strong><\/span>
\n<\/p>\n
\nTwo right circular cones x and y are made, x having three times the radius of y and y having half the volume of x. Calculate the ratio between the heights of x and y.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\nThe diameters of two cones are equal. If their slant heights are in the ratio 5:4, find the ratio of their curved surface areas.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\nThere are two cones. The curved surface area of one is twice that of the other. The slant height of the latter is twice that of the former. Find the ratio of their radii.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\nA heap of wheat is in the form of a cone of diameter 16.8 m and height 3.5 m. Find its volume. How much cloth is required to just cover the heap?
\nSolution:<\/strong><\/span>
\n<\/p>\n
\nFind what length of canvas, 1.5 m in width, is required to make a conical tent 48 m in diameter and 7 m in height. Given that 10% of the canvas is used in folds and stitching. Also, find the cost of the canvas at the rate of Rs. 24 per meter.
\nSolution:<\/strong><\/span>
\n
\n<\/p>\n
\nA solid cone of height 8 cm and base radius 6 cm is melted and re-casted into identical cones, each of height 2 cm and diameter 1 cm. Find the number of cones formed.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\n
\nSolution:<\/strong><\/span>
\n<\/p>\n
\n
\nSolution:<\/strong><\/span>
\n<\/p>\n
\nA vessel, in the form of an inverted cone, is filled with water to the brim. Its height is 32 cm and diameter of the base is 25.2 cm. Six equal solid cones are dropped in it, so that they are fully submerged. As a result, one-fourth of water in the original cone overflows. What is the volume of each of the solid cones submerged?
\nSolution:<\/strong><\/span>
\n<\/p>\n
\n
\nSolution:<\/strong><\/span>
\n<\/p>\nCylinder, Cone and Sphere Surface Area and Volume Exercise 20C –\u00a0Selina Concise Mathematics Class 10 ICSE Solutions<\/h3>\n
\n
\nSolution:<\/strong><\/span>
\n<\/p>\n
\n
\nSolution:<\/strong><\/span>
\n<\/p>\n
\nA spherical ball of lead has been melted and made into identical smaller balls with radius equal to half the radius of the original one. How many such balls can be made?
\nSolution:<\/strong><\/span>
\n<\/p>\n
\nHow many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 cm.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\n8 metallic sphere; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere.
\nSolution:<\/strong><\/span>
\n<\/p>\n
\nThe volume of one sphere is 27 times that of another sphere. Calculate the ratio of their:
\n(i) radii
\n(ii) surface areas
\nSolution:<\/strong><\/span>
\n<\/p>\n