Mensuration II (Volumes and Surface Areas of a Cuboid and a Cube) Exercise 21.1

Question: 1

Find the volume of a cuboid whose:

i) Length = 12 cm, breadth = 8 cm and height = 6 cm

ii) length = 1.2 m, breadth = 30 cm ,height = 15 cm

iii)  length = 1.5 dm, breadth = 2.5 dm, height = 8 cm

Solution:

i) In the given cuboid, we have:

Length = 12 cm, breadth = 8 cm and height = 6 cm

Therefore,  Volume of the cuboid = length x breadth x height =12 x 8 x 6 = 576 cm³

Therefore,  Volume of the cuboid = 576 cm³

ii) In the given cuboid, we have :

length = 1.2 m = 1.2 x 100 cm ( 1 m = 100 cm ) = 120 cm

breadth = 30 cm

height = 15 cm

Therefore, Volume of the cuboid = length x breadth x height = 120 x 30 x 15 = 54000 cm³

Therefore, Volume of the cuboid = 54000 cm³

iii) In the given cuboid, we have :

length = 1.5 dm = 1.5 x 10 ( 1 dm = 10 cm ) = 15 cm

breadth = 2.5 dm =2.5 x 10 cm =25 cm

height = 8 cm

Therefore, Volume of cuboid = length x breadth x height = 15 x 25 x 8 = 3000 cm³

Therefore, Volume of cuboid = 3000 cm³

Question: 2

Find the volume of cube whose side is:

i) 4 cm

ii) 8 cm

iii) 1.5 dm

iv) 1.2 m

v) 25 mm

Solution:

i) The side of the given cube is 4 cm

Therefore, Volume of the cube = ( side )³ = ( 4 )³ = 64 cm³

Volume of the cube = 64 cm³

ii) The side of the given cube is 8 cm

Therefore, Volume of the cube = ( side )³ = ( 8 )³ = 512 cm³

Volume of the cube = 512 cm³

iii) The side of the given cube is 1.5 dm = 1.5 dm x 10 cm = 15 cm

Therefore, Volume of the cube = ( side )³ = ( 15 )³ = 3375 cm³

Volume of the cube = 3375 cm³

iv) The side of the given cube is 1.2 m = 1.2 m x 100 = 120 cm

Therefore, Volume of the cube = ( side )³ = ( 120 )³ = 1728000 cm³

Volume of the cube = 1728000 cm³

v) The side of the given cube is 25 mm = 25 mm x 0.1 = 2.5 cm

Therefore, Volume of the cube = ( side )³ = ( 2.5 )³ = 15.625 cm³

Volume of the cube = 15.625 cm³

Question: 3

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

Solution:

Question: 4

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

Solution:

Let h cm be the height of the cuboidal vessel.

Given : Length = 10 cm

Breadth = 5 cm

Volume of the vessel = 300 cm³

Now, volume of a cuboid = length x breadth x height

300 = 10 x 5 x h

300 = 50 x h

Question: 5

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

Solution:

Question: 6

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

Solution:

Question: 7

What will happen to the volume of the cube , if its edge is :

i) Halved

ii) Trebled?

Solution:

Question: 8

What will happen to the volume of cuboid if its :

i) Length is doubled, height is same and breadth is halved?

ii) length is doubled, height is doubled and breadth is same?

Solution:

Question: 9

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

Solution:

Question: 10

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

Solution:

Question: 11

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?

Solution:

Question: 12

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.

Solution:

Question: 13

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.

Solution:

Question: 14

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.

Solution:

Question: 15

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 ?

Solution:

Question: 16

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 ?

Solution:

Question: 17

Suppose that there are two cubes, having edges 2 cm and 4 cm, respectively. Find volumes V1 and V2 of the cubes and compare them.

Solution:

Question: 18

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

Solution:

Question: 19

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.

Solution:

The weight of the metal block of dimension 5 cm x 4 cm x 3 cm is 1 kg.

Its volume = length x breadth x height = (5 x 4 x 3) cm³ = 60 cm³

i.e. , the weight of 60 cm³ of the metal is 1 kg

Again, the dimension of the other block which is of same metal is 15 cm x 8 cm x 3 cm.

Its volume = length x breadth x height = ( 15 x 8 x 3 ) cm³ = 360 cm³

Therefore, The weight of the required block = 360 cm³ = 6 x 60 cm³ ( therefore, Weight of 60 cm³ of the metal is 1 Kg ) = 6 x 1 kg = 6 kg

Question: 20

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

Solution:

Question: 21

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

Solution: