NCERT solutions for Mathematics Exemplar Class 9 chapter 13 - Surface Area & Volumes [Latest edition]

Chapter 13: Surface Area & Volumes

Exercise 13.1Exercise 13.2Exercise 13.3Exercise 13.4
Exercise 13.1 [Pages 122 - 123]

NCERT solutions for Mathematics Exemplar Class 9 Chapter 13 Surface Area & Volumes Exercise 13.1 [Pages 122 - 123]

Choose the correct alternative:

Exercise 13.1 | Q 1 | Page 122

The radius of a sphere is 2r, then its volume will be ______.

• 4/3 pir^3

• 4pir^3

• (8pir^3)/3

• 32/3pir^3

Exercise 13.1 | Q 2 | Page 122

The total surface area of a cube is 96 cm2. The volume of the cube is ______.

• 8 cm3

• 512 cm3

• 64 cm

• 27 cm3

Exercise 13.1 | Q 3 | Page 122

A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is ______.

• 4.2 cm

• 2.1 cm

• 2.4 cm

• 1.6 cm

Exercise 13.1 | Q 4 | Page 122

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

• Halved

• Doubled

• Same

• Four time

Exercise 13.1 | Q 5 | Page 123

The total surface area of a cone whose radius is r/2 and slant height 2l is ______.

• 2pir (l + r)

• pir (l + r/4)

• pir(l + r)

• 2pirl

Exercise 13.1 | Q 6 | Page 123

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

• 10:17

• 20:27

• 17:27

• 20:37

Exercise 13.1 | Q 7 | Page 123

The lateral surface area of a cube is 256 m2. The volume of the cube is ______.

• 512 m3

• 64 m3

• 216 m3

• 256 m3

Exercise 13.1 | Q 8 | Page 123

The number of planks of dimensions (4 m × 50 cm × 20 cm) that can be stored in a pit which is 16 m long, 12m wide and 4 m deep is ______.

• 1900

• 1920

• 1800

• 1840

Exercise 13.1 | Q 9 | Page 123

The length of the longest pole that can be put in a room of dimensions (10 m × 10 m × 5m) is ______.

• 15 m

• 16 m

• 10 m

• 12 m

Exercise 13.1 | Q 10 | Page 123

The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is ______.

• 1:4

• 1:3

• 2:3

• 2:1

Exercise 13.2 [Page 124]

NCERT solutions for Mathematics Exemplar Class 9 Chapter 13 Surface Area & Volumes Exercise 13.2 [Page 124]

State whether the following statement is True or False:

Exercise 13.2 | Q 1 | Page 124

The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.

• True

• False

Exercise 13.2 | Q 2 | Page 124

If the radius of a right circular cone is halved and height is doubled, the volume will remain unchanged.

• True

• False

Exercise 13.2 | Q 3 | Page 124

In a right circular cone, height, radius and slant height do not always be sides of a right triangle.

• True

• False

Exercise 13.2 | Q 4 | Page 124

If the radius of a cylinder is doubled and its curved surface area is not changed, the height must be halved.

• True

• False

Exercise 13.2 | Q 5 | Page 124

The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius r.

• True

• False

Exercise 13.2 | Q 6 | Page 124

A cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone.

• True

• False

Exercise 13.2 | Q 7 | Page 124

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is 1:2:3.

• True

• False

Exercise 13.2 | Q 8 | Page 124

If the length of the diagonal of a cube is 6sqrt(3) cm, then the length of the edge of the cube is 3 cm.

• True

• False

Exercise 13.2 | Q 9 | Page 124

If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be 6 : π.

• True

• False

Exercise 13.2 | Q 10 | Page 124

If the radius of a cylinder is doubled and height is halved, the volume will be doubled.

• True

• False

Exercise 13.3 [Pages 126 - 127]

NCERT solutions for Mathematics Exemplar Class 9 Chapter 13 Surface Area & Volumes Exercise 13.3 [Pages 126 - 127]

Exercise 13.3 | Q 1 | Page 126

Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16 cm × 8 cm × 8 cm. When 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. [Use π = 3.14]

Exercise 13.3 | Q 2 | Page 126

A storage tank is in the form of a cube. When it is full of water, the volume of water is 15.625 m3. If the present depth of water is 1.3 m, find the volume of water already used from the tank.

Exercise 13.3 | Q 3 | Page 126

Find the amount of water displaced by a solid spherical ball of diameter 4.2 cm, when it is completely immersed in water.

Exercise 13.3 | Q 4 | Page 126

How many square metres of canvas is required for a conical tent whose height is 3.5 m and the radius of the base is 12 m?

Exercise 13.3 | Q 5 | Page 127

Two solid spheres made of the same metal have weights 5920 g and 740 g, respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is 5 cm.

Exercise 13.3 | Q 6 | Page 127

A school provides milk to the students daily in a cylindrical glasses of diameter 7 cm. If the glass is filled with milk upto an height of 12 cm, find how many litres of milk is needed to serve 1600 students.

Exercise 13.3 | Q 7 | Page 127

A cylindrical roller 2.5 m in length, 1.75 m in radius when rolled on a road was found to cover the area of 5500 m2. How many revolutions did it make?

Exercise 13.3 | Q 8 | Page 127

A small village, having a population of 5000, requires 75 litres of water per head per day. The village has got an overhead tank of measurement 40 m × 25 m × 15 m. For how many days will the water of this tank last?

Exercise 13.3 | Q 9 | Page 127

Exercise 13.3 | Q 10 | Page 127

A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. Find the volume and the curved surface of the solid so formed.

Exercise 13.4 [Pages 127 - 128]

NCERT solutions for Mathematics Exemplar Class 9 Chapter 13 Surface Area & Volumes Exercise 13.4 [Pages 127 - 128]

Exercise 13.4 | Q 1 | Page 127

A cylindrical tube opened at both the ends is made of iron sheet which is 2 cm thick. If the outer diameter is 16 cm and its length is 100 cm, find how many cubic centimeters of iron has been used in making the tube?

Exercise 13.4 | Q 2 | Page 127

A semi-circular sheet of metal of diameter 28 cm is bent to form an open conical cup. Find the capacity of the cup.

Exercise 13.4 | Q 3.(i) | Page 128

A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5 m. How many students can sit in the tent if a student, on an average, occupies 5/7 m2 on the ground?

Exercise 13.4 | Q 3.(ii) | Page 128

A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5 m. Find the volume of the cone.

Exercise 13.4 | Q 4 | Page 128

The water for a factory is stored in a hemispherical tank whose internal diameter is 14 m. The tank contains 50 kilolitres of water. Water is pumped into the tank to fill to its capacity. Calculate the volume of water pumped into the tank.

Exercise 13.4 | Q 5 | Page 128

The volumes of the two spheres are in the ratio 64:27. Find the ratio of their surface areas.

Exercise 13.4 | Q 6 | Page 128

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

Exercise 13.4 | Q 7 | Page 128

A sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceed its height?

Exercise 13.4 | Q 8.(i) | Page 128

30 circular plates, each of radius 14 cm and thickness 3cm are placed one above the another to form a cylindrical solid. Find the total surface area

Exercise 13.4 | Q 8.(ii) | Page 128

30 circular plates, each of radius 14 cm and thickness 3cm are placed one above the another to form a cylindrical solid. Find volume of the cylinder so formed.

Chapter 13: Surface Area & Volumes

Exercise 13.1Exercise 13.2Exercise 13.3Exercise 13.4

NCERT solutions for Mathematics Exemplar Class 9 chapter 13 - Surface Area & Volumes

NCERT solutions for Mathematics Exemplar Class 9 chapter 13 (Surface Area & Volumes) 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 Exemplar Class 9 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics Exemplar Class 9 chapter 13 Surface Area & Volumes are Surface Area of a Cube, Surface Area of a Cuboid, Surface Area of Cylinder, Surface Area of a Right Circular Cone, Surface Area of a Sphere, Volume of a Cuboid, Volume of a Cylinder, Volume of a Right Circular Cone, Volume of a Sphere.

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