#### Chapters

Chapter 2: Exponents of Real Numbers

Chapter 3: Rationalisation

Chapter 4: Algebraic Identities

Chapter 5: Factorisation of Algebraic Expressions

Chapter 6: Factorisation of Polynomials

Chapter 7: Linear Equations in Two Variables

Chapter 8: Co-ordinate Geometry

Chapter 9: Introduction to Euclid’s Geometry

Chapter 10: Lines and Angles

Chapter 11: Triangle and its Angles

Chapter 12: Congruent Triangles

Chapter 13: Quadrilaterals

Chapter 14: Areas of Parallelograms and Triangles

Chapter 15: Circles

Chapter 16: Constructions

Chapter 17: Heron’s Formula

Chapter 18: Surface Areas and Volume of a Cuboid and Cube

Chapter 19: Surface Areas and Volume of a Circular Cylinder

Chapter 20: Surface Areas and Volume of A Right Circular Cone

Chapter 21: Surface Areas and Volume of a Sphere

Chapter 22: Tabular Representation of Statistical Data

Chapter 23: Graphical Representation of Statistical Data

Chapter 24: Measures of Central Tendency

Chapter 25: Probability

## Chapter 19: Surface Areas and Volume of a Circular Cylinder

#### RD Sharma solutions for Mathematics for Class 9 Chapter 19 Surface Areas and Volume of a Circular Cylinder Exercise 19.1 [Pages 8 - 9]

Curved surface area of a right circular cylinder is 4.4 `m^2`. If the radius of the base of the cylinder is 0.7 m, find its height.

In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.

A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of 12.50 per `m^2`.

It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square meters of the sheet are required for the same?

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

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.

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.

The inner diameter of a circular well is 3.5 m. It is 10 m deep Find:

(i) inner curved surface area.

(ii) the cost of plastering this curved surface at the rate of Rs. `40 per m^2`

The students of a Vidyalaya were asked to participate in a competition for making and decorating pen holders in the shape of a cylinder with a base, using cardboard. Each pen holder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition?

The diameter of roller 1.5 m long is 84 cm. If it takes 100 revolutions to level a playground, find the cost of levelling this ground at the rate of 50 paise per square metre.

Twenty 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?

A solid cylinder has total surface area of 462 cm2. Its curved surface area is one-third of its total surface area. Find the radius and height of the cylinder.

The total surface area of a hollow metal cylinder, open at both ends of external radius 8 cm and height 10 cm is 338 p `cm^2`. Taking r to be inner radius, obtain an equation in r and use it to obtain the thickness of the metal in the cylinder.

Find the lateral curved surface area of a cylinderical petrol storage tank that is 4.2 m in diameter and 4.5 m high. How much steel was actually used, if `1/12` of steel actually used was wasted in making the closed tank?

#### RD Sharma solutions for Mathematics for Class 9 Chapter 19 Surface Areas and Volume of a Circular Cylinder Exercise 19.2 [Pages 20 - 22]

A soft drink is available in two packs-(i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and (ii) a plastic cylinder with circular base diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?

The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20 cm and height 10 m. How much concrete mixture would be required to build 14 such pillars?

The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm^{3} of wood has a mass of 0.6 gm.

If the lateral surface of a cylinder is 94.2 cm^{2} and its height is 5 cm, find:

(i) radius of its base

(ii) volume of the cylinder

[Use ` pi` = 3.14]

The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?

A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to server 250 patients?

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.

The cost of painting the total outside surface of a closed cylindrical oil tank at 50 paise per square decimetre is Rs 198. The height of the tank is 6 times the radius of the base of the tank. Find the volume corrected to 2 decimal places.

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 and the ratio of their curved surfaces.

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 cm^{2}.

The curved surface area of a cylinder is 1320 cm^{2} and its base had diameter 21 cm. Find the height and the volume of the cylinder.

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, it its volume is 1617 cm^{3}.

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

The curved surface area of a cylindrical pillar is 264 m^{2} and its volume is 924 m^{3}. Find the diameter and the height of the pillar.

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

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.

How many cubic metres of earth must be dugout to sink a well 21 m deep and 6 m diameter? Find the cost of plastering the inner surface of the well at Rs 9.50 per m^{2}

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

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.

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.

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.

A rectangular sheet of paper 30 cm × 18 cm can be transformed into the curved surfaced 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.

How many litres of water flow out of a pipe having an area of cross-section of 5cm^{2} in one minute, if the speed of water in the pipe is 30 cm/ sec?

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.

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

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

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.

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.

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?

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?

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 cm^{2}. Find the volume of the cylinder.

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.

#### RD Sharma solutions for Mathematics for Class 9 Chapter 19 Surface Areas and Volume of a Circular Cylinder [Page 28]

Write the number of surfaces of a right circular cylinder.

Write the ratio of total surface area to the curved surface area of a cylinder of radius *r*and height *h.*

The ratio between the radius of the base and height of a cylinder is 2 : 3. If its volume is 1617 cm^{3}, find the total surface area of the cylinder.

If the radii of two cylinder are in the ratio 2 : 3 and their heights are in the ratio 5 : 3, then find the ratio of their volumes.

#### RD Sharma solutions for Mathematics for Class 9 Chapter 19 Surface Areas and Volume of a Circular Cylinder [Pages 28 - 30]

Mark the correct alternative in each of the following:

In a cylinder, if radius is doubled and height is halved, curved surface area will be

halved

doubled

same

four times

Two cylindrical jars have their diameters in the ratio 3 : 1, but height 1 : 3. Then the ratio of their volumes is

1 : 4

1 : 3

3 : 1

2 : 5

The number of surfaces in right cylinder is

1

2

3

4

Vertical cross-section of a right circular cylinder is always a

square

rectangle

rhombus

trapezium

If r is the radius and h is height of the cylinder the volume will be

- \[\frac{1}{3} \pi r^2 h\]
\[\pi r^2 h\]

- \[\pi r (h + r)\]
\[\pi r h\]

The number of surfaces of a hollow cylindrical object is

1

2

3

4

If the radius of a cylinder is doubled and the height remains same, the volume will be

doubled

halved

same

four times

If the height of a cylinder is doubled and radius remains the same, then volume will be

doubled

halved

same

four times

In a cylinder, if radius is halved and height is doubled, the volume will be

same

doubled

halved

four times

If the diameter of the base of a closed right circular cylinder be equal to its height h, then its whole surface area is

- \[2 \pi h^2\]
\[\frac{3}{2} \pi h^2\]

- \[\frac{4}{3} \pi h^2\]
\[\pi h^2\]

A right circular cylindrical tunnel of diameter 2 m and length 40 m is to be constructed from a sheet of iron. The area of the iron sheet required in m^{2}, is

40 \[\pi\]

80 \[\pi\]

160 \[\pi\]

200 \[\pi\]

Two circular cylinders of equal volume have their heights in the ratio 1 : 2 Ratio of their radii is

- \[1 : \sqrt{2}\]
- \[\sqrt{2}: 1\]
1 : 2

1 : 4

The radius of a wire is decreased to one-third. If volume remains the same, the length will become

3 times

6 times

9 times

27 times

If the height of a cylinder is doubled, by what number must the radius of the base be multiplied so that the resulting cylinder has the same volume as the original cylinder?

4

- \[\frac{1}{\sqrt{2}}\]
2

- \[\frac{1}{2}\]

The volume of a cylinder of radius r is 1/4 of the volume of a rectangular box with a square base of side length* x*. If the cylinder and the box have equal heights, what is *r* in terms of *x*?

- \[\frac{x^2}{2\pi}\]
- \[\frac{x}{2\sqrt{\pi}}\]
- \[\frac{\sqrt{2x}}{\pi}\]
\[\frac{\pi}{2\sqrt{x}}\]

The height *h* of a cylinder equals the circumference of the cylinder. In terms of *h* what is the volume of the cylinder?

A cylinder with radius r and height h is closed on the top and bottom. Which of the following expressions represents the total surface area of this cylinder?

- \[2\pi r (r + h)\]
- \[\pi r (r + 2h)\]
- \[\pi r + (2r + h)\]
\[2 \pi r^2 + h\]

The height of sand in a cylindrical shaped can drops 3 inches when 1 cubic foot of sand is poured out. What is the diameter, in inches, of the cylinder?

- \[\frac{24}{\pi}\]
- \[\frac{48}{\pi}\]
- \[\frac{32}{\pi}\]
- \[\frac{48}{\pi}\]

Two steel sheets each of length a_{1} and breadth a_{2} are used to prepare the surfaces of two right circular cylinders ⇀ one having volume v_{1} and height a_{2} and other having volume v_{2} and height a_{1}. Then,

*v*_{1}=*v*_{2}*a*_{1}*v*_{1}=*a*_{2}*v*_{2}*a*_{2}*v*_{1}=*a*_{1}*v*_{2}- \[\frac{v_1}{a_1} = \frac{v_2}{a_2}\]

The altitude of a circular cylinder is increased six times and the base area is decreased one-ninth of its value. The factor by which the lateral surface of the cylinder increases, is

- \[\frac{2}{3}\]
- \[\frac{1}{2}\]
- \[\frac{3}{2}\]
2

## Chapter 19: Surface Areas and Volume of a Circular Cylinder

## RD Sharma solutions for Mathematics for Class 9 chapter 19 - Surface Areas and Volume of a Circular Cylinder

RD Sharma solutions for Mathematics for Class 9 chapter 19 (Surface Areas and Volume of a 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 9 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics for Class 9 chapter 19 Surface Areas and Volume of a Circular Cylinder are Surface Area of a Sphere, Volume of a Cuboid, Volume of a Cylinder, Volume of a Right Circular Cone, Volume of a Sphere, Surface Area of a Cuboid and a Cube, Surface Area of a Right Circular Cylinder, Surface Area of a Right Circular Cone.

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