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RD Sharma solutions for Class 8 Mathematics chapter 22 - Mensuration - III (Surface Area and Volume of a Right Circular Cylinder)

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RD Sharma Mathematics Class 8 by R D Sharma (2019-2020 Session)

Mathematics for Class 8 by R D Sharma (2019-2020 Session) - Shaalaa.com

Chapter 22: Mensuration - III (Surface Area and Volume of a Right Circular Cylinder)

Ex. 22.10Ex. 22.20

Chapter 22: Mensuration - III (Surface Area and Volume of a Right Circular Cylinder) Exercise 22.10 solutions [Pages 10 - 11]

Ex. 22.10 | Q 1 | Page 10

Find the curved surface area and total surface area of a cylinder, the diameter of whose base is 7 cm and height is 60 cm.

 
Ex. 22.10 | Q 2 | Page 10

The curved surface area of a cylindrical road is 132 cm2. Find its length if the radius is 0.35 cm.

 
Ex. 22.10 | Q 3 | Page 10

The area of the base of a right circular cylinder is 616 cm2 and its height is 2.5 cm. Find the curved surface area of the cylinder.

 
Ex. 22.10 | Q 4 | Page 10

The circumference of the base of a cylinder is 88 cm and its height is 15 cm. Find its curved surface area and total surface area.

 
Ex. 22.10 | Q 5 | Page 10

A rectangular strip 25 cm × 7 cm is rotated about the longer side. Find The total surface area of the solid thus generated.

 
Ex. 22.10 | Q 6 | Page 10

A rectangular sheet of paper, 44 cm × 20 cm, is rolled along its length to form a cylinder. Find the total surface area of the cylinder thus generated.

 
Ex. 22.10 | Q 7 | Page 10

The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. Calculate the ratio of their curved surface areas.

 
Ex. 22.10 | Q 8 | Page 10

The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Prove that its height and radius are equal.

 
Ex. 22.10 | Q 9 | Page 11

The curved surface area of a cylinder is 1320 cm2 and its base has diameter 21 cm. Find the height of the cylinder.

 
Ex. 22.10 | Q 10 | Page 11

The height of a right circular cylinder is 10.5 cm. If three times the sum of the areas of its two circular faces is twice the area of the curved surface area. Find the radius of its base. 

Ex. 22.10 | Q 11 | Page 11

Find the cost of plastering the inner surface of a well at Rs 9.50 per m2, if it is 21 m deep and diameter of its top is 6 m.

Ex. 22.10 | Q 12 | Page 11

A cylindrical vessel open at the top has diameter 20 cm and height 14 cm. Find the cost of tin-plating it on the inside at the rate of 50 paise per hundred square centimetre.

 
Ex. 22.10 | Q 13 | Page 11

The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find the cost of plastering its inner curved surface at Rs 4 per square metre.

 
Ex. 22.10 | Q 14 | Page 11

The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions moving once over to level a playground. What is the area of the playground?

Ex. 22.10 | Q 15 | Page 11

Twenty one cylindrical pillars of the Parliament House are to be cleaned. If the diameter of each pillar is 0.50 m and height is 4 m, what will be the cost of cleaning them at the rate of Rs 2.50 per square metre?

 
Ex. 22.10 | Q 16 | Page 11

The total surface area of a hollow cylinder which is open from both sides is 4620 sq. cm, area of base ring is 115.5 sq. cm and height 7 cm. Find the thickness of the cylinder.

 
Ex. 22.10 | Q 17 | Page 11

The sum of the radius of the base and height of a solid cylinder is 37 m. If the total surface area of the solid cylinder is 1628 m2, find the circumference of its base.

 
Ex. 22.10 | Q 18 | Page 11

Find the ratio between the total surface area of a cylinder to its curved surface area, given that its height and radius are 7.5 cm and 3.5 cm.

 
Ex. 22.10 | Q 19 | Page 11

A cylindrical vessel, without lid, has to be tin-coated on its both sides. If the radius of the base is 70 cm and its height is 1.4 m, calculate the cost of tin-coating at the rate of Rs 3.50 per 1000 cm2.

 

Chapter 22: Mensuration - III (Surface Area and Volume of a Right Circular Cylinder) Exercise 22.20 solutions [Pages 25 - 27]

Ex. 22.20 | Q 1.1 | Page 25

Find the volume of a cylinder whose r = 3.5 cm, h = 40 cm .

Ex. 22.20 | Q 1.2 | Page 25

Find the volume of a cylinder whose  r = 2.8 m, h = 15 m .

Ex. 22.20 | Q 2.1 | Page 25

Find the volume of a cylinder, if the diameter (d) of its base and its altitude (h) are: d = 21 cm, h = 10 cm .

Ex. 22.20 | Q 2.2 | Page 25

Find the volume of a cylinder, if the diameter (d) of its base and its altitude (h) are:  d = 7 m, h = 24 m .

Ex. 22.20 | Q 3 | Page 25

The area of the base of a right circular cylinder is 616 cm2 and its height is 25 cm. Find the volume of the cylinder.

 
Ex. 22.20 | Q 4 | Page 25

The circumference of the base of a cylinder is 88 cm and its height is 15 cm. Find the volume of the cylinder.

 
Ex. 22.20 | Q 5 | Page 25

A hollow cylindrical pipe is 21 dm long. Its outer and inner diameters are 10 cm and 6 cm respectively. Find the volume of the copper used in making the pipe.

 
Ex. 22.20 | Q 6.1 | Page 25

Find the  curved surface area whose height is 15 cm and the radius of the base is 7 cm.

Ex. 22.20 | Q 6.2 | Page 25

Find the  total surface area and   whose height is 15 cm and the radius of the base is 7 cm. 

Ex. 22.20 | Q 6.3 | Page 25

Find the volume of a right circular cylinder whose height is 15 cm and the radius of the base is 7 cm.

Ex. 22.20 | Q 7 | Page 25

The diameter of the base of a right circular cylinder is 42 cm and its height is 10 cm. Find the volume of the cylinder.

Ex. 22.20 | Q 8 | Page 25

Find the volume of a cylinder, the diameter of whose base is 7 cm and height being 60 cm. Also, find the capacity of the cylinder in litres.

Ex. 22.20 | Q 9 | Page 25

A rectangular strip 25 cm × 7 cm is rotated about the longer side. Find the volume of the solid, thus generated.

Ex. 22.20 | Q 10 | Page 25

A rectangular sheet of paper, 44 cm × 20 cm, is rolled along its length to form a cylinder. Find the volume of the cylinder so formed.

Ex. 22.20 | Q 11 | Page 25

The volume and the curved surface area of a cylinder are 1650 cm3 and 660 cm2respectively. Find the radius and height of the cylinder.

Ex. 22.20 | Q 12 | Page 25

The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. Calculate the ratio of their volumes.

Ex. 22.20 | Q 13 | Page 25

The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Find the volume of the cylinder, if its total surface area is 616 cm2.

Ex. 22.20 | Q 14 | Page 25

The curved surface area of a cylinder is 1320 cm2 and its base has diameter 21 cm. Find the volume of the cylinder.

Ex. 22.20 | Q 15 | Page 25

The ratio between the radius of the base and the height of a cylinder is 2 : 3. Find the total surface area of the cylinder, if its volume is 1617 cm3.

Ex. 22.20 | Q 16 | Page 25

The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the diameter and the height of the pillar.

Ex. 22.20 | Q 17 | Page 25

Two circular cylinders of equal volumes have their heights in the ratio 1 : 2. Find the ratio of their radii.

Ex. 22.20 | Q 18 | Page 25

The height of a right circular cylinder is 10.5 m. Three times the sum of the areas of its two circular faces is twice the area of the curved surface. Find the volume of the cylinder.

Ex. 22.20 | Q 19 | Page 25

How many cubic metres of earth must be dug-out to sink a well 21 m deep and 6 m diameter?

Ex. 22.20 | Q 20 | Page 26

The trunk of a tree is cylindrical and its circumference is 176 cm. If the length of the trunk is 3 m, find the volume of the timber that can be obtained from the trunk.

Ex. 22.20 | Q 21 | Page 26

A well is dug 20 m deep and it has a diameter of 7 m. The earth which is so dug out is spread out on a rectangular plot 22 m long and 14 m broad. What is the height of the platform so formed?

Ex. 22.20 | Q 22 | Page 26

A well with 14 m diameter is dug 8 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. Find the height of the embankment.

Ex. 22.20 | Q 23 | Page 26

A cylindrical container with diameter of base 56 cm contains sufficient water to submerge a rectangular solid of iron with dimensions 32 cm × 22 cm × 14 cm. Find the rise in the level of the water when the solid is completely submerged.

Ex. 22.20 | Q 24 | Page 26

A rectangular sheet of paper 30 cm × 18 cm can be transformed into the curved surface of a right circular cylinder in two ways i.e., either by rolling the paper along its length or by rolling it along its breadth. Find the ratio of the volumes of the two cylinders thus formed.

Ex. 22.20 | Q 25 | Page 25

The rain which falls on a roof 18 m long and 16.5 m wide is allowed to be stored in a cylindrical tank 8 m in diameter. If it rains 10 cm on a day, what is the rise of water level in the tank due to it?

Ex. 22.20 | Q 26 | Page 26

A piece of ductile metal is in the form of a cylinder of diameter 1 cm and length 5 cm. It is drawnout into a wire of diameter 1 mm. What will be the length of the wire so formed?

Ex. 22.20 | Q 27 | Page 26

Find the length of 13.2 kg of copper wire of diameter 4 mm, when 1 cubic cm of copper weighs 8.4 gm.

Ex. 22.20 | Q 28 | Page 26

2.2 cubic dm of brass is to be drawn into a cylindrical wire 0.25 cm in diameter. Find the length of the wire.

Ex. 22.20 | Q 29 | Page 26

The difference between inside and outside surfaces of a cylindrical tube 14 cm long is 88 sq. cm. If the volume of the tube is 176 cubic cm, find the inner and outer radii of the tube.

Ex. 22.20 | Q 30 | Page 26

Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 metres per second into a cylindrical tank, the radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes?

Ex. 22.20 | Q 31 | Page 26

A cylindrical tube, open at both ends, is made of metal. The internal diameter of the tube is 10.4 cm and its length is 25 cm. The thickness of the metal is 8 mm everywhere. Calculate the volume of the metal

Ex. 22.20 | Q 32 | Page 26

From a tap of inner radius 0.75 cm, water flows at the rate of 7 m per second. Find the volume in litres of water delivered by the pipe in one hour.

Ex. 22.20 | Q 33 | Page 26

A cylindrical water tank of diameter 1.4 m and height 2.1 m is being fed by a pipe of diameter 3.5 cm through which water flows at the rate of 2 metre per second. In how much time the tank will be filled?

Ex. 22.20 | Q 34 | Page 26

A rectangular sheet of paper 30 cm × 18 cm can be transformed into the curved surface of a right circular cylinder in two ways i.e., either by rolling the paper along its length or by rolling it along its breadth. Find the ratio of the volumes of the two cylinders thus formed.

Ex. 22.20 | Q 35 | Page 26

How many litres of water flow out of a pipe having an area of cross-section of 5 cm2 in one minute, if the speed of water in the pipe is 30 cm/sec?

Ex. 22.20 | Q 36 | Page 26

A solid cylinder has a total surface area of 231 cm2. Its curved surface area is \[\frac{2}{3}\] of the total surface area. Find the volume of the cylinder.

Ex. 22.20 | Q 37 | Page 27

Find the cost of sinking a tubewell 280 m deep, having diameter 3 m at the rate of Rs 3.60 per cubic metre. Find also the cost of cementing its inner curved surface at Rs 2.50 per square metre.

Ex. 22.20 | Q 38 | Page 27

Find the length of 13.2 kg of copper wire of diameter 4 mm, when 1 cubic cm of copper weighs 8.4 gm.

Ex. 22.20 | Q 39 | Page 27

2.2 cubic dm of brass is to be drawn into a cylindrical wire 0.25 cm in diameter. Find the length of the wire.

Ex. 22.20 | Q 40 | Page 27

A well with 10 m inside diameter is dug 8.4 m deep. Earth taken out of it is spread all around it to a width of 7.5 m to form an embankment. Find the height of the embankment.

Ex. 22.20 | Q 41 | Page 27

A hollow garden roller, 63 cm wide with a girth of 440 cm, is made of 4 cm thick iron. Find the volume of the iron.

Ex. 22.20 | Q 42 | Page 27

What length of a solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of length 16 cm, external diameter 20 cm and thickness 2.5 mm?

Ex. 22.20 | Q 43 | Page 27

In the middle of a rectangular field measuring 30m × 20m, a well of 7 m diameter and 10 m depth is dug. The earth so removed is evenly spread over the remaining part of the field. Find the height through which the level of the field is raised.

Chapter 22: Mensuration - III (Surface Area and Volume of a Right Circular Cylinder)

Ex. 22.10Ex. 22.20

RD Sharma Mathematics Class 8 by R D Sharma (2019-2020 Session)

Mathematics for Class 8 by R D Sharma (2019-2020 Session) - Shaalaa.com

RD Sharma solutions for Class 8 Mathematics chapter 22 - Mensuration - III (Surface Area and Volume of a Right Circular Cylinder)

RD Sharma solutions for Class 8 Maths chapter 22 (Mensuration - III (Surface Area and Volume of a Right Circular Cylinder)) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics for Class 8 by R D Sharma (2019-2020 Session) solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 8 Mathematics chapter 22 Mensuration - III (Surface Area and Volume of a Right Circular Cylinder) are Area of Trapezium, Area of a General Quadrilateral, Area of a Polygon, Concept of Solid Shapes, Concept of Cuboid, Concept of Cube, Concept of Cylinders, Conept of Cylinder, Volume and Capacity, Introduction of Mensuration, Concept of Cuboid, Concept of Cube.

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