#### 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 : Introduction to Euclid’s Geometry

Chapter 8 : Lines and Angles

Chapter 9 : Triangle and its Angles

Chapter 10 : Congruent Triangles

Chapter 11 : Co-ordinate Geometry

Chapter 12 : Heron’s Formula

Chapter 13 : Linear Equations in Two Variables

Chapter 14 : Quadrilaterals

Chapter 15 : Areas of Parallelograms and Triangles

Chapter 16 : Circles

Chapter 17 : Constructions

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 21 : Surface Areas and Volume of a Sphere

#### Page 8

Find the surface area of a sphere of radius 10.5 cm .

Find the surface area of a sphere of radius 5.6 cm .

Find the surface area of a sphere of radius 14 cm .

Find the surface area of a sphere of diameter 14 cm .

Find the surface area of a sphere of diameter 21 cm .

Find the surface area of a sphere of diameter 3.5 cm .

Find the total surface area of a hemisphere and a solid hemisphere each of radius 10 cm.

(Use 𝜋 = 3.14)

The surface area of a sphere is 5544 `cm^2`, find its diameter.

A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin- plating

it on the inside at the rate of Rs. 4 per 100 `cm^2`

The dome of a building is in the form of a hemisphere. Its radius is 63 dm. Find the cost of

painting it at the rate of Rs. 2 per sq. m.

Assuming the earth to be a sphere of radius 6370 km, how many square kilo metres is area

of the land, if three-fourth of the earth’s surface is covered by water?

A cylinder of same height and radius is placed on the top of a hemisphere. Find the curved

surface area of the shape if the length of the shape be 7 cm.

A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base

of the cone is 16 cm and its height is 15 cm. Find the cost of painting the toy at Rs. 7 per 100

`cm^2`.

A storage tank consists of a circular cylinder with a hemisphere adjoined on either end. If the

external diameter of the cylinder be 1.4 m and its length be 8 m, find the cost of painting it

on the outside at the rate of Rs. 10 per `m^2`.

The diameter of the moon is approximately one fourth of the diameter of the earth. Find the

ratio of their surface areas.

A hemi-spherical dome of a building needs to be painted. If the circumference of the base of

the dome is 17.6 cm, find the cost of painting it, given the cost of painting is Rs. 5 per l00

`cm^2`

The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in the given figure. Eight such spheres are used for this purpose, and are to be painted silver. Each support is a cylinder of radius 1.5 cm and height 7 cm and is to be painted black. Find the cost of paint required if silver paint costs 25 paise per cm^{2} and black paint costs 5 paise per cm^{2}.

#### Pages 19 - 21

Find the volume of a sphere whose radius is 2 cm.

Find the volume of a sphere whose radius is 3.5 cm.

Find the volume of a sphere whose radius is 10.5 cm .

Find the volume of a sphere whose diameter is 14 cm .

Find the volume of a sphere whose diameter is 3.5 dm .

Find the volume of a sphere whose diameter is 2.1 m .

A hemispherical tank has inner radius of 2.8 m. Find its capacity in litres.

A hemispherical bowl is made of steel 0.25 cm thick. The inside radius of the bowl is 5 cm. Find the volume of steel used in making the bowl.

How mañy bullets can be made out of a cube of lead, whose edge measures 22 cm, each bullet being 2 cm in diameter?

A shopkeeper has one laddoo of radius 5 cm. With the same material, how many laddoos of radius 2.5 cm can be made .

A spherical ball of lead 3 cm in diameter is melted and recast into three spherical balls. If the diameters of two balls be `a/2`cm and 2 cm, find the diameter of the third ball.

A sphere of radius 5 cm is immersed in water filled in a cylinder, the level of water rises `5/a`cm. Find the radius of the cylinder.

If the radius of a sphere is doubled, what is the ratio of the volume of the first sphere to that of the second sphere?

A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.

A vessel in the form of a hemispherical bowl is full of water. Its contents are emptied in a right circular cylinder. The internal radii of the bowl and the cylinder are 3.5 cm and 7 cm respectively. Find the height to which the water will rise in the cylinder.

A cylinder whose height is two thirds of its diameter, has the same volume as a sphere of radius 4 cm. Calculate the radius of the base of the cylinder.

A vessel in the form of a hemispherical bowl is full of water. The contents are emptied into a cylinder. The internal radii of the bowl and cylinder are respectively 6 cm and 4 cm. Find the height of water in the cylinder

A cylindrical tub of radius 16 cm contains water to a depth of 30 cm. A spherical iron ball is dropped into the tub and thus level of water is raised by 9 cm. What is the radius of the ball?

A cylinder of radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the cylinder and thus the level of water is raised by 6.75 cm. Find the radius of the ball.

(Use 𝜋 = 22/7).

The diameter of a coper sphere is 18 cm. The sphere is melted and is drawn into a long wire of uniform circular cross-section. If the length of the wire is 108 m, find its diameter.

A cylindrical jar of radius 6 cm contains oil. Iron spheres each of radius 1 .5 cm are immersed in the oil. How many spheres are necessary to raise the level of the oil by two centimetres?

A measuring jar of internal diameter 10 cm is partially filled with water. Four equal spherical balls of diameter 2 cm each are dropped in it and they sink down in water completely. What will be the change in the level of water in the jar?

The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of the wire.

The radius of the internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm respectively. If it is melted and recast into a solid cylinder of heigh2`2/a`cm Find the diameter of the cylinder.

A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49 cm. Find the radius of the base.

A hollow sphere of internal and external radii 2 cm and 4 cm respectively is melted into a cone of base radius 4 cm. Find the height and slant height of the cone.

A metallic sphere of radius 10.5 cm is melted and thus recast into small cones, each of radius 3.5 cm and height 3 cm. Find how many cones are obtained.

A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Show that their volumes are in the ratio 1 : 2 : 3.

A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical form ball is dropped into the tub and thus the level of water is raised by 6.75 cm. What is the radius of the ball?

The largest sphere is carved out of a cube of side 10.5 cm. Find the volume of the sphere.

A sphere, a cylinder and a cone have the same diameter. The height of the cylinder and also the cone are equal to the diameter of the sphere. Find the ratio of their volumes.

A cube of side 4 cm contains a sphere touching its side. Find the volume of the gap in between.

A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.

A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine `("in " mm^3)` is needed to fill this capsule?

The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

#### Textbook solutions for Class 9

## RD Sharma solutions for Class 9 Mathematics chapter 21 - Surface Areas and Volume of a Sphere

RD Sharma solutions for Class 9 Maths chapter 21 (Surface Areas and Volume of a Sphere) 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 by R D Sharma (2018-19 Session) solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 9 Mathematics chapter 21 Surface Areas and Volume of a Sphere are Volume of a Sphere, Volume of a Right Circular Cone, Volume of a Cylinder, Volume of a Cuboid, Surface Area of a Sphere, Surface Area of a Right Circular Cone, Surface Area of a Right Circular Cylinder, Surface Area of a Cuboid and a Cube.

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