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# RD Sharma solutions for Class 9 Mathematics chapter 18 - Surface Areas and Volume of a Cuboid and Cube

## Mathematics for Class 9 by R D Sharma (2018-19 Session)

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

Ex. 18.1Ex. 18.2Others

#### Chapter 18: Surface Areas and Volume of a Cuboid and Cube Exercise 18.1 solutions [Pages 14 - 15]

Ex. 18.1 | Q 1 | Page 14

Find the lateral surface area and total surface area of a cuboid of length 80 cm, breadth 40 cm and height 20 cm.

Ex. 18.1 | Q 2 | Page 14

Find the lateral surface area and total surface area of a cube of edge 10 cm.

Ex. 18.1 | Q 3 | Page 14

Find the ratio of the total surface area and lateral surface area of a cube.

Ex. 18.1 | Q 4 | Page 14

Mary wants to decorate her Christmas tree. She wants to place the tree on a wooden block
covered with coloured paper with picture of Santa Claus on it. She must know the exact
quantity of paper to buy for this purpose. If the box has length, breadth and height as 80
cm, 40 cm and 20 cm respectively. How many square sheets of paper of side 40 cm would
she require?

Ex. 18.1 | Q 5 | Page 14

The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost
of white washing the walls of the room and the ceiling at the rate of Rs. 7.50 m2.

Ex. 18.1 | Q 6 | Page 14

Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new cuboid to that of the sum of the surface areas of the three cubes.

Ex. 18.1 | Q 7 | Page 14

A 4 cm cube is cut into 1 cm cubes. Calculate the total surface area of all the small cubes.

Ex. 18.1 | Q 8 | Page 14

The length of a hall is 18 m and the width 12 m. The sum of the areas of the floor and the
flat roof is equal to the sum of the areas of the four walls. Find the height of the hall.

Ex. 18.1 | Q 9 | Page 14

Hameed has built a cubical water tank with lid for his house, with each other edge 1 .5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm. Find how much he would spend for the tiles, if the cost of tiles is Rs. 360 per dozen.

Ex. 18.1 | Q 10 | Page 14

Each edge of a cube is increased by 50%. Find the percentage increase in the surface area of the cube.

Ex. 18.1 | Q 11 | Page 14

A closed iron tank 12 m long, 9 m wide and 4 m deep is to be made. Determine the cost of iron sheet used at the rate of Rs. 5 per metre sheet, sheet being 2 m wide.

Ex. 18.1 | Q 12 | Page 14

Ravish wanted to make a temporary shelter for his car by making a box-like structure with tarpaulin that covers all the four sides and the top of the car ( with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m with
base dimensions 4 m × 3m?

Ex. 18.1 | Q 13 | Page 14

An open box is made of wood 3 cm thick. Its external length, breadth and height are 1.48 m, 1.16 m and 8.3 m. Find the cost of painting the inner surface of Rs 50 per sq. metre.

Ex. 18.1 | Q 14 | Page 14

The dimensions of a room are 12.5 m by 9 m by 7 m. There are 2 doors and 4 windows in the room; each door measures 2.5 m by 1 .2 m and each window 1 .5 m by I m. Find the cost of painting the walls at Rs. 3.50 per square metre.

Ex. 18.1 | Q 15 | Page 15

The paint in a certain container is sufficient to paint on area equal to 9.375 m2. How manybricks of dimension 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?

Ex. 18.1 | Q 16 | Page 15

The dimensions of a rectangular box are in the ratio of 2 : 3 : 4 and the difference between the cost ofcovering it with sheet of paper at the rates of Rs. 8 and Rs. 9.50 per m2 is Rs.1248. Find the dimensions of the box.

Ex. 18.1 | Q 17 | Page 15

The cost of preparing the walls of a room 12 m long at the rate of Rs. 1.35 per square metre is Rs. 340.20 and the cost of matting the floor at 85 paise per square metre is Rs. 91.80. Find the height of the room.

Ex. 18.1 | Q 18 | Page 15

The length and breadth of a hall are in the ratio 4: 3 and its height is 5.5 metres. The cost of decorating its walls (including doors and windows) at Rs. 6.60 per square metre is Rs. 5082. Find the length and breadth of the room.

Ex. 18.1 | Q 19 | Page 15

A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm (See Fig. 18.5). The thickness of the plank is 5 cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per cm2 and the rate of painting is 10 paise per cm2. Find the total expenses required for polishing and painting the surface of the bookshelf.

#### Chapter 18: Surface Areas and Volume of a Cuboid and Cube Exercise 18.2 solutions [Pages 29 - 31]

Ex. 18.2 | Q 1 | Page 29

A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold?

Ex. 18.2 | Q 2 | Page 29

A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?

Ex. 18.2 | Q 3 | Page 29

Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per m3.

Ex. 18.2 | Q 4 | Page 29

If the area of three adjacent faces of a cuboid are 8 cm^2, 18 cm^3 and 25 cm^3. Find the
volume of the cuboid.

Ex. 18.2 | Q 5 | Page 29

The breadth of a room is twice its height, one half of its length and the volume of the room is 512cu. m. Find its dimensions.

Ex. 18.2 | Q 6 | Page 29

Three metal cubes with edges 6 cm, 8 cm and 10 cm respectively are melted together and formed into a single cube. Find the volume, surface area and diagonal of the new cube.

Ex. 18.2 | Q 7 | Page 30

Two cubes, each of volume 512 cm3 are joined end to end. Find the surface area of the resulting cuboid.

Ex. 18.2 | Q 8 | Page 30

A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of the two smaller cubes are 6 cm and 8 cm, find the edge of the third smaller cube.

Ex. 18.2 | Q 9 | Page 30

The dimensions of a cinema hall are 100 m, 50 m and 18 m. How many persons can sit in the hall, if each person requires 150 m^3 of air?

Ex. 18.2 | Q 10 | Page 30

Given that 1 cubic cm of marble weighs 0.25 kg, the weight of marble block 28 cm in width and 5 cm thick is 112 kg. Find the length of the block.

Ex. 18.2 | Q 11 | Page 30

A box with lid is made of 2 cm thick wood. Its external length, breadth and height are 25 cm, 18 cm and 15 cm respectively. How much cubic cm of a liquid can be placed in it? Also, find the volume of the wood used in it.

Ex. 18.2 | Q 12 | Page 30

The external dimensions of a closed wooden box are 48 cm, 36 cm, 30 cm. The box is made of 1.5 cm thick wood. How many bricks of size 6 cm x 3 cm x 0.75 cm can be put in this box?

Ex. 18.2 | Q 13 | Page 30

A cube of 9 cm edge is immersed completely in a rectangular vessel containing water. Ifthe dimensions of the base are 15 cm and 12 cm, find the rise in water level in the vessel.

Ex. 18.2 | Q 14 | Page 30

A field is 200 m long and 150 m broad. There is a plot, 50 m long and 40 m broad, near thefield. The plot is dug 7 m deep and the earth taken out is spread evenly on the field. Byhow many meters is the level of the field raised? Give the answer to the second place of decimal.

Ex. 18.2 | Q 15 | Page 30

A field is in the form of a rectangle of length 18 m and width 15 m. A pit, 7.5 m long, 6 m broad and 0.8 m deep, is dug in a corner of the field and the earth taken out is spread over the remaining area of the field. Find out the extent to which the level of the field has been raised.

Ex. 18.2 | Q 16 | Page 30

A village having a population of 4000 requires 150 litres of water per head per day. It has a tank measuring 20 m × 15 m × 6 m. For how many days will the water of this tank last?

Ex. 18.2 | Q 17 | Page 30

A child playing with building blocks, which are of the shape of the cubes, has built a structure as shown in Fig. 18.12 If the edge of each cube is 3 cm, find the volume of the structure built by the child.

Ex. 18.2 | Q 18 | Page 31

A godown measures 40m × 25 m × 10 m. Find the maximum number of wooden crates each measuring 1.5 m
× 1.25 m × 0.5 m that can be stored in the godown.

Ex. 18.2 | Q 19 | Page 31

A wall of length 10 m was to be built across an open ground. The height of the wall is 4 m and thickness of the wall is 24 cm. If this wall is to be built up with bricks whose dimensions are 24 cm × 12 cm × 8 cm, How many bricks would be required?

Ex. 18.2 | Q 20 | Page 31

If V is the volume of a cuboid of dimensions a, b, c and S is its surface area, then prove that

1/V=2/S(1/a+1/b+1)

Ex. 18.2 | Q 21 | Page 31

The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V, prove that
V^2 = xyz

Ex. 18.2 | Q 22 | Page 31

A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?

Ex. 18.2 | Q 23 | Page 31

Water in a canal 30 cm wide and 12 cm deep, is flowing with a velocity of l00 km per hour.How much area will it irrigate in 30 minutes if 8 cm of standing water is desired?

Ex. 18.2 | Q 24 | Page 31

Water in a rectangular reservoir having base 80 m by 60 m i s 6.5 m deep. In what time can the water be emptied by a pipe ôf which the cross-section is a square of side 20 cm, if the water runs through the pipe at the rate of 15 km/hr.

Ex. 18.2 | Q 24 | Page 31

Half cubic meter of gold-sheet is extended by hammering so as to cover an area of 1 hectare. Find the thickness of the gold-sheet.

Ex. 18.2 | Q 25 | Page 31

How many cubic centimeters of iron are there in an open box whose external dimensions are 36 cm, 25 cm and I 6.5 cm, the iron being 1.5 cm thick throughout? If I cubic cm of iron weighs 15g, find the weight of the empty box in kg.

Ex. 18.2 | Q 26 | Page 31

A rectangular container, whose base is a square of side 5 cm, stands on a horizontal table, and holds water up to 1 cm from the top. When a cube is placed in the water it is completely submerged, the water rises to the top and 2 cubic cm of water overflows. Calculate the volume of the cube and also the length of its edge.

Ex. 18.2 | Q 27 | Page 31

A rectangular tank is 80 m long and 25 m broad. Water flows into it through a pipe whose cross-section is 25 cm2, at the rate of 16 km per hour. How much the level of the water rises in the tank in 45 minutes.

#### Chapter 18: Surface Areas and Volume of a Cuboid and Cube solutions [Page 35]

Q 1 | Page 35

If two cubes each of side 6 cm are joined face to face, then find the volume of the resulting cuboid.

Q 2 | Page 35

Three cubes of metal whose edges are in the ratio 3 : 4 : 5 are melted down in to a single cube whose diagonal is 12 sqrt(3) cm. Find the edges of three cubes.

Q 2.2 | Page 35

Find the edge of a cube whose surface area is 432 m2.

Q 3 | Page 35

If the perimeter of each face of a cube is 32 cm, find its lateral surface area. Note that four faces which meet the base of a cube are called its lateral faces.

Q 3.2 | Page 35

If the length of a diagonal of a cube is 8 sqrt(3) cm, then its surface area is

• 512 cm2

•  384 cm2

• 192 cm2

•  768 cm2

Q 4 | Page 35

If the volumes of two cubes are in the ratio 8: 1, then the ratio of their edges is

• 8 : 1

• 2sqrt(2):1

• 2 : 1

•  none of these

Q 5 | Page 35

A cuboid has total surface area of 372 cm2 and its lateral surface area is 180 cm2, find the area of its base.

Q 5.2 | Page 35

The volume of a cube whose surface area is 96 cm2, is

• 16sqrt(2) cm^3

• 32 cm3

• 64 cm3

•  216 cm3

Q 6 | Page 35

Three cubes of each side 4 cm are joined end to end. Find the surface area of the resulting cuboid.

Q 6.2 | Page 35

The length, width and height of a rectangular solid are in the ratio of 3 : 2 : 1. If the volume of the box is 48cm3, the total surface area of the box is

•  27 cm2

•  32 cm2

• 44 cm2

• 88 cm2

Q 7 | Page 35

The surface area of a cuboid is 1300 cm2. If its breadth is 10 cm and height is 20 cm2, find its length.

Q 7.2 | Page 35

If the areas of the adjacent faces of a rectangular block are in the ratio 2 : 3 : 4 and its volume is 9000 cm3, then the length of the shortest edge is

•  30 cm

• 20 cm

•  15 cm

•  10 cm

#### Chapter 18: Surface Areas and Volume of a Cuboid and Cube solutions [Pages 35 - 37]

Q 2 | Page 35

The length of the longest rod that can be fitted in a cubical vessel of edge 10 cm long, is

• 10 cm

• 10sqrt(2) cm

• 10sqrt(3) cm

• 20 cm

Q 4 | Page 35

Three equal cubes are placed adjacently in a row. The ratio of the total surface area of the resulting cuboid to that of the sum of the surface areas of three cubes, is

• 7 : 9

• 49 : 81

• 9 : 7

• 27 : 23

Q 8 | Page 36

If each edge of a cube, of volume V, is doubled, then the volume of the new cube is

• 2 V

• 4 V

•  6 V

• 8 V

Q 9 | Page 36

If each edge of a cuboid of surface area S is doubled, then surface area of the new cuboid is

•  2 S

• 4 S

• 6 S

• 8 S

Q 10 | Page 36

The area of the floor of a room is 15 m2. If its height is 4 m, then the volume of the air contained in the room is

•  60 dm3

•  600 dm3

•  6000 dm3

• 60000 dm3

Q 11 | Page 36

The cost of constructing a wall 8 m long, 4 m high and 10 cm thick at the rate of Rs. 25 per m3 is

•  Rs. 16

•  Rs. 80

• Rs. 160

• Rs. 320

Q 12 | Page 36

10 cubic metres clay is uniformly spread on a land of area 10 ares. the rise in the level of the ground is

• 1 cm

•  10 cm

•  100 cm

• 1000 cm

Q 13 | Page 36

Volume of a cuboid is 12 cm3. The volume (in cm3) of a cuboid whose sides are double of the above cuboid is

• 24

• 48

• 72

• 96

Q 14 | Page 36

If the sum of all the edges of a cube is 36 cm, then the volume (in cm3) of that cube is

• 9

• 27

• 219

• 729

Q 15 | Page 36

The number of cubes of side 3 cm that can be cut from a cuboid of dimensions 10 cm × 9 cm × 6 cm, is

• 9

• 10

• 18

• 20

Q 16 | Page 36

On a particular day, the rain fall recorded in a terrace 6 m long and 5 m broad is 15 cm. The quantity of water collected in the terrace is

•  300 litres

•  450 litres

• 3000 litres

•  4500 litres

Q 17 | Page 36

If A1, A2, and A3 denote the areas of three adjacent faces of a cuboid, then its volume is

• A1 A2 A3

• 2A1 A2 A3

• $\sqrt{A_1 A_2 A_3}$

• ${}^3 \sqrt{A_1 A_2 A_3}$

Q 18 | Page 36

If l is the length of a diagonal of a cube of volume V, then

• 3V = l3

• sqrt(3V )= 1^3

• 3 sqrt(3V )= 21^3

• 3sqrt(3V )= 1^3

Q 19 | Page 36

If V is the volume of a cuboid of dimensions xyz and A is its surface area, then A/V

•  x2y2z2

• $\frac{1}{2}\left( \frac{1}{xy} + \frac{1}{yz} + \frac{1}{zx} \right)$

• $\left( \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \right)$

• $\frac{1}{xyz}$

Q 20 | Page 36

The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is  5 sqrt(5) cm. Its surface area is

•  361 cm2

• 125 cm2

•  236 cm2

• 486 cm2

Q 21 | Page 36

If each edge of a cube is increased by 50%, the percentage increase in its surface area is

• 50%

•  75%

• 100%

•  125%

Q 22 | Page 37

A cube whose volume is 1/8 cubic centimeter is placed on top of a cube whose volume is 1 cm3. The two cubes are then placed on top of a third cube whose volume is 8 cm3. The height of the stacked cubes is

• 3.5 cm

• 3 cm

• 7 cm

• none of these

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

Ex. 18.1Ex. 18.2Others

## RD Sharma solutions for Class 9 Mathematics chapter 18 - Surface Areas and Volume of a Cuboid and Cube

RD Sharma solutions for Class 9 Maths chapter 18 (Surface Areas and Volume of a Cuboid and Cube) 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 18 Surface Areas and Volume of a Cuboid and Cube 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 Cuboid and Cube 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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