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# RD Sharma solutions for Class 8 Mathematics chapter 21 - Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube)

## Chapter 21: Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube)

Ex. 21.10Ex. 21.20Ex. 21.30Ex. 21.40

#### Chapter 21: Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube) Exercise 21.10 solutions [Pages 8 - 9]

Ex. 21.10 | Q 1.1 | Page 8

Find the volume of a cuboid whose length = 12 cm, breadth = 8 cm, height = 6 cm.

Ex. 21.10 | Q 1.2 | Page 8

Find the volume of a cuboid whose  length =1.2 m, breadth = 30 cm, height = 15 cm.

Ex. 21.10 | Q 1.3 | Page 8

Find the volume of a cuboid whose length = 15 cm, breadth = 2.5 dm, height = 8 cm.

Ex. 21.10 | Q 2.1 | Page 8

Find the volume of a cube whose side is 4 cm .

Ex. 21.10 | Q 2.2 | Page 8

Find the volume of a cube whose side is 8 cm .

Ex. 21.10 | Q 2.3 | Page 8

Find the volume of a cube whose side is 1.5 dm .

Ex. 21.10 | Q 2.4 | Page 8

Find the volume of a cube whose side is 1.2 m .

Ex. 21.10 | Q 2.5 | Page 8

Find the volume of a cube whose side is 25 mm .

Ex. 21.10 | Q 3 | Page 8

Find the height of a cuboid of volume 100 cm3, whose length and breadth are 5 cm and 4 cm respectively.

Ex. 21.10 | Q 4 | Page 8

A cuboidal vessel is 10 cm long and 5 cm wide. How high it must be made to hold 300 cm3 of a liquid?

Ex. 21.10 | Q 5 | Page 8

A milk container is 8 cm long and 50 cm wide. What should be its height so that it can hold 4 litres of milk?

Ex. 21.10 | Q 6 | Page 8

A cuboidal wooden block contains 36 cm3 wood. If it be 4 cm long and 3 cm wide, find its height.

Ex. 21.10 | Q 7.1 | Page 8

What will happen to the volume of a cube, if its edge is halved ?

Ex. 21.10 | Q 7.2 | Page 8

What will happen to the volume of a cube, if its edge is trebled?

Ex. 21.10 | Q 8.1 | Page 8

What will happen to the volume of a cuboid if its Length is doubled, height is same and breadth is halved?

Ex. 21.10 | Q 8.2 | Page 8

What will happen to the volume of a cuboid if its Length is doubled, height is doubled and breadth is sama?

Ex. 21.10 | Q 9 | Page 8

Three cuboids of dimensions 5 cm × 6 cm × 7cm, 4cm × 7cm × 8 cm and 2 cm × 3 cm × 13 cm are melted and a cube is made. Find the side of cube.

Ex. 21.10 | Q 10 | Page 8

Find the weight of solid rectangular iron piece of size 50 cm × 40 cm × 10cm, if 1 cm3 of iron weighs 8 gm.

Ex. 21.10 | Q 11 | Page 8

How many wooden cubical blocks of side 25 cm can be cut from a log of wood of size 3 m by 75 cm by 50 cm, assuming that there is no wastage?

Ex. 21.10 | Q 12 | Page 8

A cuboidal block of silver is 9 cm long, 4 cm broad and 3.5 cm in height. From it, beads of volume 1.5 cm3 each are to be made. Find the number of beads that can be made from the block.

Ex. 21.10 | Q 13 | Page 8

Find the number of cuboidal boxes measuring 2 cm by 3 cm by 10 cm which can be stored in a carton whose dimensions are 40 cm, 36 cm and 24 cm.

Ex. 21.10 | Q 14 | Page 8

A cuboidal block of solid iron has dimensions 50 cm, 45 cm and 34 cm. How many cuboids of size 5 cm by 3 cm by 2 cm can be obtained from this block? Assume cutting causes no wastage.

Ex. 21.10 | Q 15 | Page 8

A cube A has side thrice as long as that of cube B. What is the ratio of the volume of cube A to that of cube B?

Ex. 21.10 | Q 16 | Page 9

An ice-cream brick measures 20 cm by 10 cm by 7 cm. How many such bricks can be stored in deep fridge whose inner dimensions are 100 cm by 50 cm by 42 cm?

Ex. 21.10 | Q 17 | Page 9

Suppose that there are two cubes, having edges 2 cm and 4 cm, respectively. Find the volumes V1and V2 of the cubes and compare them.

Ex. 21.10 | Q 18 | Page 9

A tea-packet measures 10 cm × 6 cm × 4 cm. How many such tea-packets can be placed in a cardboard box of dimensions 50 cm × 30 cm × 0.2 m?

Ex. 21.10 | Q 19 | Page 9

The weight of a metal block of size 5 cm by 4 cm by 3 cm is 1 kg. Find the weight of a block of the same metal of size 15 cm by 8 cm by 3 cm.

Ex. 21.10 | Q 20 | Page 9

How many soap cakes can be placed in a box of size 56 cm × 0.4 m × 0.25 m, if the size of a soap cake is 7 cm × 5 cm × 2.5 cm?

Ex. 21.10 | Q 21 | Page 9

The volume of a cuboidal box is 48 cm3. If its height and length are 3 cm and 4 cm respectively, find its breadth.

#### Chapter 21: Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube) Exercise 21.20 solutions [Pages 15 - 16]

Ex. 21.20 | Q 1.1 | Page 15

Find the volume in cubic metre (cu. m) of the cuboid whose dimensions is length = 12 m, breadth = 10 m, height = 4.5 cm.

Ex. 21.20 | Q 1.2 | Page 15

Find the volume in cubic metre (cu. m) of the cuboid whose dimensions islength = 4 m, breadth = 2.5 m, height = 50 cm.

Ex. 21.20 | Q 1.3 | Page 15

Find the volume in cubic metre (cu. m) of the cuboid whose dimensions is length = 10 m, breadth = 25 dm, height = 50 cm.

Ex. 21.20 | Q 2.1 | Page 15

Find the volume in cubic decimetre of the cube whose side is 1.5 m.

Ex. 21.20 | Q 2.2 | Page 15

Find the volume in cubic decimetre of the cube whose side is 75 cm.

Ex. 21.20 | Q 2.3 | Page 15

Find the volume in cubic decimetre of the cube whose side is 2 dm 5 cm .

Ex. 21.20 | Q 3 | Page 15

How much clay is dug out in digging a well measuring 3 m by 2 m by 5 m?

Ex. 21.20 | Q 4 | Page 15

What will be the height of a cuboid of volume 168 m3, if the area of its base is 28 m2?

Ex. 21.20 | Q 5 | Page 15

A tank is 8 m long, 6 m broad and 2 m high. How much water can it contain?

Ex. 21.20 | Q 6 | Page 15

The capacity of a certain cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its height and length are 10 m and 2.5 m respectively.

Ex. 21.20 | Q 7 | Page 15

A rectangular diesel tanker is 2 m long, 2 m wide and 40 cm deep. How many litres of diesel can it hold?

Ex. 21.20 | Q 8 | Page 15

The length , breadth and height of a room are 5 m, 4.5 m and 3 m, respectively. Find the volume of the air it contains.

Ex. 21.20 | Q 9 | Page 15

A water tank is 3 m long, 2 m broad and 1 m deep. How many litres of water can it hold?

Ex. 21.20 | Q 10 | Page 15

How many planks each of which is 3 m long, 15 cm broad and 5 cm thick can be prepared from a wooden block 6 m long, 75 cm broad and 45 cm thick?

Ex. 21.20 | Q 11 | Page 15

How many bricks each of size 25 cm × 10 cm × 8 cm will be required to build a wall 5 m long, 3 m high and 16 cm thick, assuming that the volume of sand and cement used in the construction is negligible?

Ex. 21.20 | Q 12 | Page 15

A village, having a population of 4000, requires 150 litres water per head per day. It has a tank which is 20 m long, 15 m broad and 6 m high. For how many days will the water of this tank last?

Ex. 21.20 | Q 13 | Page 15

A rectangular field is 70 m long and 60 m broad. A well of dimensions 14 m × 8 m × 6 m is dug outside the field and the earth dug-out from this well is spread evenly on the field. How much will the earth level rise?

Ex. 21.20 | Q 14 | Page 15

A swimming pool is 250 m long and 130 m wide. 3250 cubic metres of water is pumped into it. Find the rise in the level of water.

Ex. 21.20 | Q 15 | Page 15

A beam 5 m long and 40 cm wide contains 0.6 cubic metre of wood. How thick is the beam?

Ex. 21.20 | Q 16 | Page 15

The rainfall on a certain day was 6 cm. How many litres of water fell on 3 hectares of field on that day?

Ex. 21.20 | Q 17 | Page 15

An 8 m long cuboidal beam of wood when sliced produces four thousand 1 cm cubes and there is no wastage of wood in this process. If one edge of the beam is 0.5 m, find the third edge.

Ex. 21.20 | Q 18 | Page 15

The dimensions of a metal block are 2.25 m by 1.5 m by 27 cm. It is melted and recast into cubes, each of the side 45 cm. How many cubes are formed?

Ex. 21.20 | Q 19 | Page 15

A solid rectangular piece of iron measures 6 m by 6 cm by 2 cm. Find the weight of this piece, if 1 cm3 of iron weighs 8 gm.

Ex. 21.20 | Q 20.01 | Page 16

Fill in the blank in the following so as to make the statement true:

1 m3 = .........cm3

Ex. 21.20 | Q 20.02 | Page 16

Fill in the blank in the following so as to make the statement true:

1 litre = ....... cubic decimetre

Ex. 21.20 | Q 20.03 | Page 16

Fill in the blank in the following so as to make the statement true:

1 kl = ....... m3

Ex. 21.20 | Q 20.04 | Page 16

Fill in the blank in the following so as to make the statement true:

The volume of a cube of side 8 cm is ........

Ex. 21.20 | Q 20.05 | Page 16

Fill in the blank in the following so as to make the statement true:

The volume of a wooden cuboid of length 10 cm and breadth 8 cm is 4000 cm3. The height of the cuboid is ........ cm.

Ex. 21.20 | Q 20.06 | Page 16

Fill in the blank in the following so as to make the statement true:

1 cu.dm = ........ cu. mm

Ex. 21.20 | Q 20.07 | Page 16

Fill in the blank in the following so as to make the statement true:

1 cu. km = ........ cu. m

Ex. 21.20 | Q 20.08 | Page 16

Fill in the blank in the following so as to make the statement true:

1 litre = ........ cu. cm

Ex. 21.20 | Q 20.09 | Page 16

Fill in the blank in the following so as to make the statement true:

1 ml = ........ cu. cm

Ex. 21.20 | Q 20.1 | Page 16

Fill in the blank in the following so as to make the statement true:

1 kl = ........ cu. dm = ........ cu. cm.

#### Chapter 21: Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube) Exercise 21.30 solutions [Pages 22 - 23]

Ex. 21.30 | Q 1.1 | Page 22

Find the surface area of a cuboid whose length = 10 cm, breadth = 12 cm, height = 14 cm.

Ex. 21.30 | Q 1.2 | Page 22

Find the surface area of a cuboid whose length = 6 dm, breadth = 8 dm, height = 10 dm.

Ex. 21.30 | Q 1.3 | Page 22

Find the surface area of a cuboid whose llength = 2 m, breadth = 4 m, height = 5 m .

Ex. 21.30 | Q 1.4 | Page 22

Find the surface area of a cuboid whoselength = 3.2 m, breadth = 30 dm, height = 250 cm.

Ex. 21.30 | Q 2.1 | Page 22

Find the surface area of a cube whose edge is 1.2 m.

Ex. 21.30 | Q 2.2 | Page 22

Find the surface area of a cube whose edge is 27 cm.

Ex. 21.30 | Q 2.3 | Page 22

Find the surface area of a cube whose edge is 3 cm.

Ex. 21.30 | Q 2.4 | Page 22

Find the surface area of a cube whose edge is 6 m .

Ex. 21.30 | Q 2.5 | Page 22

Find the surface area of a cube whose edge is 2.1 m.

Ex. 21.30 | Q 3 | Page 22

A cuboidal box is 5 cm by 5 cm by 4 cm. Find its surface area.

Ex. 21.30 | Q 4.1 | Page 22

Find the surface area of a cube whose volume is  343 m3.

Ex. 21.30 | Q 4.2 | Page 22

Find the surface area of a cube whose volume is  216 dm3.

Ex. 21.30 | Q 5.1 | Page 22

Find the volume of a cube whose surface area is  96 cm2.

Ex. 21.30 | Q 5.2 | Page 22

Find the volume of a cube whose surface area is 150 m2 .

Ex. 21.30 | Q 6 | Page 22

The dimensions of a cuboid are in the ratio 5 : 3 : 1 and its total surface area is 414 m2. Find the dimensions.

Ex. 21.30 | Q 7 | Page 22

Find the area of the cardboard required to make a closed box of length 25 cm, 0.5 m and height 15 cm.

Ex. 21.30 | Q 8 | Page 22

Find the surface area of a wooden box whose shape is of a cube, and if the edge of the box is 12 cm.

Ex. 21.30 | Q 9 | Page 22

The dimensions of an oil tin are 26 cm × 26 cm × 45 cm. Find the area of the tin sheet required for making 20 such tins. If 1 square metre of the tin sheet costs Rs 10, find the cost of tin sheet used for these 20 tins.

Ex. 21.30 | Q 10 | Page 22

A cloassroom is 11 m long, 8 m wide and 5 m high. Find the sum of the areas of its floor and the four walls (including doors, windows, etc.)

Ex. 21.30 | Q 11 | Page 22

A swimming pool is 20 m long 15 m wide and 3 m deep. Find the cost of repairing the floor and wall at the rate of Rs 25 per square metre.

Ex. 21.30 | Q 12 | Page 22

The perimeter of a floor of a room is 30 m and its height is 3 m. Find the area of four walls of the room.

Ex. 21.30 | Q 13 | Page 22

Show that the product of the areas of the floor and two adjacent walls of a cuboid is the square of its volume.

Ex. 21.30 | Q 14 | Page 22

The walls and ceiling of a room are to be plastered. The length, breadth and height of the room are 4.5 m, 3 m and 350 cm, respectively. Find the cost of plastering at the rate of Rs 8 per square metre.

Ex. 21.30 | Q 15 | Page 23

A cuboid has total surface area of 50 m2 and lateral surface area is 30 m2. Find the area of its base.

Ex. 21.30 | Q 16 | Page 23

A classroom is 7 m long, 6 m broad and 3.5 m high. Doors and windows occupy an area of 17 m2. What is the cost of white-washing the walls at the rate of Rs 1.50 per m2.

Ex. 21.30 | Q 17 | Page 23

The central hall of a school is 80 m long and 8 m high. It has 10 doors each of size 3 m × 1.5 m and 10 windows each of size 1.5 m × 1 m. If the cost of white-washing the walls of the hall at the rate of Rs 1.20 per m2 is Rs 2385.60, fidn the breadth of the hall.

#### Chapter 21: Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube) Exercise 21.40 solutions [Pages 30 - 31]

Ex. 21.40 | Q 1 | Page 30

Find the length of the longest rod that can be placed in a room 12 m long, 9 m broad and 8 m high.

Ex. 21.40 | Q 2 | Page 30

If V is the volume of a cuboid of dimensions a, b, c and S is its surface area, then prove that $\frac{1}{V} = \frac{2}{S}\left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right)$

Ex. 21.40 | Q 3 | Page 30

The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V, prove that V2 = xyz.

Ex. 21.40 | Q 4 | Page 30

A rectangular water reservoir contains 105 m3 of water. Find the depth of the water in the reservoir if its base measures 12 m by 3.5 m.

Ex. 21.40 | Q 5 | Page 30

Cubes A, B, C having edges 18 cm, 24 cm and 30 cm respectively are melted and moulded into a new cube D. Find the edge of the bigger cube D.

Ex. 21.40 | Q 6 | Page 30

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

Ex. 21.40 | Q 7 | Page 30

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. 21.40 | Q 8 | Page 30

A tank open at the top is made of iron sheet 4 m wide. If the dimensions of the tank are 12 m × 8 m × 6 m, find the cost of iron sheet at Rs 17.50 per metre.

Ex. 21.40 | Q 9 | Page 30

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. 21.40 | Q 10 | Page 30

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 1 m. Find the cost of painting the walls at Rs 3.50 per square metre.

Ex. 21.40 | Q 11 | Page 30

A field is 150 m long and 100 m wide. A plot (outside the field) 50 m long and 30 m wide is dug to a depth of 8 m and the earth taken out from the plot is spread evenly in the field. By how much is the level of field raised?

Ex. 21.40 | Q 12 | Page 30

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

Ex. 21.40 | Q 13 | Page 30

Three cubes whose edges measure 3 cm, 4 cm, and 5 cm respectively are melted to form a new cube. Find the surface area of the new cube formed.

Ex. 21.40 | Q 14 | Page 30

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. 21.40 | Q 15 | Page 30

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 wall.

Ex. 21.40 | Q 16 | 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. 21.40 | Q 17 | 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 m3 of air?

Ex. 21.40 | Q 18 | 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 × 3 cm × 0.75 cm can be put in this box?

Ex. 21.40 | Q 19 | Page 31

The dimensions of a rectangular box are in the ratio of 2 : 3 : 4 and the difference between the cost of covering 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.

## Chapter 21: Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube)

Ex. 21.10Ex. 21.20Ex. 21.30Ex. 21.40

## RD Sharma solutions for Class 8 Mathematics chapter 21 - Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube)

RD Sharma solutions for Class 8 Maths chapter 21 (Mensuration - II (Volumes and Surface Areas of a Cuboid and a 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 8 by R D Sharma (2019-2020 Session) solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 8 Mathematics chapter 21 Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube) are Area of Trapezium, Area of a General Quadrilateral, Area of a Polygon, Concept of Solid Shapes, Concept of Cuboid, Concept of Cube, Concept of Cylinders, Conept of Cylinder, Volume and Capacity, Introduction of Mensuration, Concept of Cuboid, Concept of Cube.

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