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

### RD Sharma solutions for Mathematics for Class 9 Chapter 18 Surface Areas and Volume of a Cuboid and CubeExercise 18.1 [Pages 14 - 15]

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

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

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

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?

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.

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.

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

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.

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.

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

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.

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?

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.

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.

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?

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.

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.

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.

A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm in following figure. 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.

### RD Sharma solutions for Mathematics for Class 9 Chapter 18 Surface Areas and Volume of a Cuboid and CubeExercise 18.2 [Pages 29 - 31]

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

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?

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 m^{3}.

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.

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.

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.

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

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.

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?

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.

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.

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?

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.

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.

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.

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?

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.

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.

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?

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)`

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

`V^2` = `xyz`

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?

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?

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.

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.

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.

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.

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.

### RD Sharma solutions for Mathematics for Class 9 Chapter 18 Surface Areas and Volume of a Cuboid and Cube [Page 35]

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

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.

Find the edge of a cube whose surface area is 432 m^{2}.

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.

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

512 cm

^{2}384 cm

^{2}192 cm

^{2}768 cm

^{2}

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

8 : 1

2`sqrt(2):1`

2 : 1

none of these

A cuboid has total surface area of 372 cm^{2} and its lateral surface area is 180 cm^{2}, find the area of its base.

The volume of a cube whose surface area is 96 cm^{2}, is

16`sqrt(2) cm^3`

32 cm

^{3}64 cm

^{3}216 cm

^{3}

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

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

27 cm

^{2}32 cm

^{2}44 cm

^{2}88 cm

^{2}

The surface area of a cuboid is 1300 cm^{2}. If its breadth is 10 cm and height is 20 cm^{2}, find its length.

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

30 cm

20 cm

15 cm

10 cm

### RD Sharma solutions for Mathematics for Class 9 Chapter 18 Surface Areas and Volume of a Cuboid and Cube [Pages 35 - 37]

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

10 cm

10`sqrt(2)` cm

10`sqrt(3)` cm

20 cm

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

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

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

The area of the floor of a room is 15 m^{2}. If its height is 4 m, then the volume of the air contained in the room is

60 dm

^{3}600 dm

^{3}6000 dm

^{3}60000 dm

^{3}

The cost of constructing a wall 8 m long, 4 m high and 10 cm thick at the rate of Rs. 25 per m^{3} is

Rs. 16

Rs. 80

Rs. 160

Rs. 320

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

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

If the sum of all the edges of a cube is 36 cm, then the volume (in cm^{3}) of that cube is

9

27

219

729

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

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

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

- \[\sqrt{A_1 A_2 A_3}\]
- \[{}^3 \sqrt{A_1 A_2 A_3}\]

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

3

*V*=*l*^{3}`sqrt(3V )= 1^3`

`3 sqrt(3V )= 21^3`

`3sqrt(3V )= 1^3`

If *V* is the volume of a cuboid of dimensions* x*, *y*, *z* and *A* is its surface area, then `A/V`

x

^{2}y^{2}z^{2}- \[\frac{1}{2}\left( \frac{1}{xy} + \frac{1}{yz} + \frac{1}{zx} \right)\]
- \[\left( \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \right)\]
- \[\frac{1}{xyz}\]

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 cm

^{2}125 cm

^{2}236 cm

^{2}486 cm

^{2}

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

50%

75%

100%

125%

A cube whose volume is 1/8 cubic centimeter is placed on top of a cube whose volume is 1 cm^{3}. The two cubes are then placed on top of a third cube whose volume is 8 cm^{3}. 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

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

RD Sharma solutions for Mathematics for Class 9 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 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 18 Surface Areas and Volume of a Cuboid and Cube 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, Surface Area of Cylinder, Surface Area of a Right Circular Cone.

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