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# RD Sharma solutions for Class 9 Mathematics chapter 20 - Surface Areas and Volume of A Right Circular Cone

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

Ex. 20.10Ex. 20.20Others

#### Chapter 20: Surface Areas and Volume of A Right Circular Cone Exercise 20.10 solutions [Pages 7 - 8]

Ex. 20.10 | Q 1 | Page 7

Find the curved surface area of a cone, if its slant height is 60 cm and the radius of its base is 21 cm.

Ex. 20.10 | Q 2 | Page 7

The radius of a cone is 5 cm and vertical height is 12 cm. Find the area of the curved surface.

Ex. 20.10 | Q 3 | Page 7

The radius of a cone is 7 cm and area of curved surface is 176 cm^2. Find the slant height.

Ex. 20.10 | Q 4 | Page 7

The height of a cone is 21 cm. Find the area of the base if the slant height is 28 cm.

Ex. 20.10 | Q 5 | Page 7

Find the total surface area of a right circular cone with radius 6 cm and height 8 cm.

Ex. 20.10 | Q 6 | Page 7

Find the curved surface area of a cone with base radius 5.25 cm and slant height 10cm.

Ex. 20.10 | Q 7 | Page 8

Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24m.

Ex. 20.10 | Q 8 | Page 8

The area of the curved surface of a cone is 60 cm2. If the slant height of the cone be 8 cm, find the radius of the base?

Ex. 20.10 | Q 9 | Page 8

The curved surface area of a cone is 4070 cm2 and its diameter is 70 cm. What is its slant height? (Use it 𝜋 = 22/7).

Ex. 20.10 | Q 10 | Page 8

The radius and slant height of a cone are In the ratio of 4 : 7. If its curved surface area is 792 cm2, find its radius. (Use it 𝜋 = 22/7).

Ex. 20.10 | Q 11 | Page 8

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.

Ex. 20.10 | Q 12 | Page 8

Find the ratio of the curved surface areas of two cones if their diameters of the bases are equal and slant heights are in the ratio 4 : 3.

Ex. 20.10 | Q 13 | Page 8

There are two cones. The curved surface area of one is twice that of the other. The slant height of the later is twice that of the former. Find the ratio of their radii.

Ex. 20.10 | Q 14 | Page 8

The diameters of two cones are equal. If their slant heights are in the ratio 5 : 4, find the ratio of their curved surfaces.

Ex. 20.10 | Q 15 | Page 8

Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find the radius of the base and total surface area of the cone.

Ex. 20.10 | Q 16 | Page 8

The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of Rs. 210 per l00 m2.

Ex. 20.10 | Q 17 | Page 8

A conical tent is 10 m high and the radius of its base is 24 m. Find the slant height of the  tent. If the cost of 1 2 m canvas is Rs. 70, find the cost of the canvas required to make the tent.

Ex. 20.10 | Q 18 | Page 8

A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground. Find the area of the canvas required for the tent.

Ex. 20.10 | Q 19 | Page 8

A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8:5, show that the radius of each is to the height of each as 3:4.

Ex. 20.10 | Q 20 | Page 8

A bus stop is barricated from the remaining part of the road, by using 50 hollow cones made of recycled card-board. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is Rs. 12 per m2, what will be the cost of painting all these cones. (Use 𝜋 = 3.14 and √1.04 = 1.02)

Ex. 20.10 | Q 21 | Page 8

What length of tarpaulin 3 m wide will be required to make a conical tent of height 8 m and base radius 6 m? Assume that the extra length of material will be required for  stitching margins and wastage in cutting is approximately 20 cm (Use it 𝜋 = 3.14)

Ex. 20.10 | Q 22 | Page 8

The circumference of the base of a 10 m height conical tent is 44 metres. Calculate the length of canvas used in making the tent if width of canvas is 2 m. (Use it 𝜋= 22/7).

Ex. 20.10 | Q 23 | Page 8

A circus tent is cylindrical to a height of 3 meters and conical above it. If its diameter is 105  m and the slant height of the conical portion is 53 m, calculate the length of the canvas 5 m
wide to make the required tent.

#### Chapter 20: Surface Areas and Volume of A Right Circular Cone Exercise 20.20 solutions [Pages 20 - 21]

Ex. 20.20 | Q 1.1 | Page 20

Find the volume of a right circular cone with:

radius 6 cm, height 7 cm.

Ex. 20.20 | Q 1.2 | Page 20

Find the volume of a right circular cone with:

radius 3.5 cm, height 12 cm

Ex. 20.20 | Q 1.3 | Page 20

Find the volume of a right circular cone with:

height 21 cm and slant height 28 cm.

Ex. 20.20 | Q 2.1 | Page 20

Find the capacity in litres of a conical vessel with radius 7 cm, slant height 25 cm

["Assume "pi=22/7]

Ex. 20.20 | Q 2.2 | Page 20

Find the capacity in litres of a conical vessel with height 12 cm, slant height 13 cm

["Assume "pi=22/7]

Ex. 20.20 | Q 3 | Page 21

Two cones have their heights in the ratio 1 : 3 and the radii of their bases in the ratio 3 : 1. Find the ratio of their volumes.

Ex. 20.20 | Q 4 | Page 21

The radius and the height of a right circular cone are in the ratio 5 : 12. If its volume is 314 cubic meter, find the slant height and the radius (Use it 𝜋 = 3.14).

Ex. 20.20 | Q 5 | Page 21

The radius and height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the slant height and radius of the cone. (Use it 𝜋 = 3.14).

Ex. 20.20 | Q 6 | Page 21

The ratio of volumes of two cones is  4 : 5 and the ratio of the radii of their bases is 2:3. Find the ratio of their vertical heights.

Ex. 20.20 | Q 7 | Page 21

A cylinder and a cone have equal radii of their bases and equal heights. Show that their volumes are in the ratio 3:1.

Ex. 20.20 | Q 8 | Page 21

If the radius of the base of a cone is halved, keeping the height same, what is the ratio of the volume of the reduced cone to that of the original cone?

Ex. 20.20 | Q 9 | Page 21

A heap of wheat is in the form of a cone of diameter 9 m and height 3.5 m. Find its volume. How much canvas cloth is required to just cover the heap? (Use 𝜋 = 3.14).

Ex. 20.20 | Q 10 | Page 21

A heap of wheat is in the form of a cone of diameter 9 m and height 3.5 m. Find its volume. How much canvas cloth is required to just cover the heap? (Use 𝜋 = 3.14).

Ex. 20.20 | Q 11 | Page 21

A right angled triangle of which the sides containing he right angle are 6.3 cm and lo cm in length, is made to turn round on the longer side. Find the volume of the solid, thus generated. Also, find its curved surface area.

Ex. 20.20 | Q 12 | Page 21

Find the volume of the largest right circular cone that can be fitted in a cube whose edge is 14 cm.

Ex. 20.20 | Q 13 | Page 21

The volume of a right circular cone is 9856 cm3. If the diameter of the base is 28 cm, find:
(i) height of the cone (ii) slant height of the cone (iii) curved surface area of the cone.

Ex. 20.20 | Q 14 | Page 21

A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilo litres?

Ex. 20.20 | Q 15 | Page 21

Monica has a piece of Canvas whose area is 551 m2. She uses it to have a conical tent made, with a base radius of 7m. Assuming that all the stitching margins and wastage incurred while cutting, amounts to approximately 1 m2. Find the volume of the tent that can be made with it.

#### Chapter 20: Surface Areas and Volume of A Right Circular Cone solutions [Pages 23 - 24]

Q 1 | Page 23

The height of a cone is 15 cm. If its volume is 500  π cm3, then find the radius of its base.

Q 2 | Page 23

If the volume of a right circular cone of height 9 cm is 48 pi  cm3, find the diameter of its base.

Q 3 | Page 23

If the height and slant height of a cone are 21 cm and 28 cm respectively. Find its volume.

Q 4 | Page 24

The height  of a conical vessel is 3.5 cm. If its capacity is 3.3 litres of milk. Find its diameter of its base.

Q 5 | Page 24

If the radius and slant height of a cone are in the ratio 7 : 13 and its curved surface area is 286 cm2, find its radius.

Q 6 | Page 24

Find the area of canvas required for a conical tent of height 24 m and base radius 7 m.

Q 7 | Page 24

Find the area of metal sheet required in making a closed hollow cone of base radius 7 cm and height 24 cm.

Q 8 | Page 24

Find the length of cloth used in making a conical pandal of height 100 m and base radius 240 m, if the cloth is 100 π m wide.

#### Chapter 20: Surface Areas and Volume of A Right Circular Cone solutions [Pages 24 - 29]

Q 1 | Page 24

Mark the correct alternative in each of the following:
The number of surfaces of a cone has, is

• 1

• 2

• 3

• 4

Q 2 | Page 24

The area of the curved surface of a cone of radius 2r and slant height 1/2, is

• pirl

• 2pirl

• 1/2pirl

• pi (r+l)r

Q 3 | Page 24

The total surface area of a cone of radius  r/2 and length 2l, is

• 2 pi r (1 + r)

•  pi r (1 + r/4)

• pi r (1+ r)

•  2 pi rl

Q 4 | Page 24

A solid cylinder is melted and cast into a cone of same radius. The heights of the cone and cylinder are in the ratio

• 9 : 1

• 1 : 9

•  3 : 1

• 1 : 3

Q 5 | Page 24

If the radius of the base of a right circular cone is 3r and its height is equal to the radius of the base, then its volume is

• 1/3 pir^3

• 2/3 pir^3

• 3 pir^3

• 9 pir^3

Q 6 | Page 24

If the volume of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5, then the ratio of their heights, is

• 1 : 5

• 5 : 4

• 5 : 16

• 25 : 64

Q 7 | Page 24

The curved surface area of one cone is twice that of the other while the slant height of the latter is twice that of the former. The ratio of their radii is

•  2 : 1

• 4 : 1

• 8 : 1

• 1 : 1

Q 8 | Page 25

If the height and radius of a cone of volume V are doubled, then the volume of the cone, is

•  3 V

•  4 V

• V

• V

Q 8 | Page 29

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

• doubled

• halved

• same

• four times

Q 9 | Page 25

The ratio of the volume of a right circular cylinder and a right circular cone of the same base and height, is

•  1 : 3

• 3 : 1

• 4 : 3

• 3 : 4

Q 9 | Page 29

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

• same

• doubled

• halved

• four times

Q 10 | Page 25

A right circular cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is

• 3 : 5

•  2 : 5

• 3 : 1

• 1 : 3

Q 10 | Page 29

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

• 2pih^2

• 3/2 pih^2

• 4/3 pih^2

• pih^2

Q 11 | Page 25

The diameters of two cones are equal. If their slant heights are in the ratio 5 : 4, the ratio of their curved surface areas, is

•  4 : 5

• 25 : 16

•  16 : 25

• 5 : 4

Q 12 | Page 25

If the heights of two cones are in the ratio of 1 : 4 and the radii of their bases are in the ratio 4 : 1, then the ratio of their volumes is

• 1 : 2

•  2 : 3

• 3 : 4

• 4 : 1

Q 13 | Page 25

The slant height of a cone is increased by 10%. If the radius remains the same, the curved surface area is increased by

• 10%

• 12.1%

•  20%

• 21%

Q 14 | Page 25

The height of a solid cone is 12 cm and the area of the circular base is 64 picm2. A plane parallel to the base of the cone cuts through the cone 9 cm above the vertex of the cone, the areas of the base of the new cone so formed is

• 9 πcm2

• 16 πcm2

•  25 πcm2

•  36 πcm

Q 15 | Page 25

If the base radius and the height of a right circular cone are increased by 20%, then the percentage increase in volume is approximately

• 60

•  68

• 73

• 78

Q 16 | Page 25

If h, S and V denote respectively  the height, curved surface area and volume of a right circular cone, then  3 pi Vh^3 - S^2h^2 + 9V^2   is equal to

• 8

• 0

• 4pi

• 32pi^2

Q 17 | Page 25

If a cone is cut into two parts by a horizontal plane passing through the mid-point of its axis, the axis, the ratio of the volumes of upper and lower part is

• 1 : 2

•  2 : 1

• 1: 7

• 1 : 8

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

Ex. 20.10Ex. 20.20Others

## RD Sharma solutions for Class 9 Mathematics chapter 20 - Surface Areas and Volume of A Right Circular Cone

RD Sharma solutions for Class 9 Maths chapter 20 (Surface Areas and Volume of A Right Circular Cone) 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.

Further, we at Shaalaa.com are providing such solutions so that students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 9 Mathematics chapter 20 Surface Areas and Volume of A Right Circular Cone 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.

Using RD Sharma Class 9 solutions Surface Areas and Volume of A Right Circular Cone exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in RD Sharma Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 9 prefer RD Sharma Textbook Solutions to score more in exam.

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