RD Sharma Solutions Class 8 Volumes Surface Area Cuboid Cube Exercise 21.2

RD Sharma Class 8 Solutions Chapter 21 Ex 21.2 PDF Free Download

RD Sharma Solutions Class 8 Chapter 21 Exercise 21.2

Exercise 21.2

Q 1. Find the volume in cubic metre ( cu .m ) of each of the cuboids whose dimensions are:

i) Length = 12 m, Breadth = 10 m , height = 4.5 m

ii) Length = 4 m, Breadth = 2.5 m , height = 50 cm

iii) Length = 10 m, Breadth = 25 dm , height = 25 cm

Soln:

i)To find the volume of a cuboid

Given: Length = 12 m

Breadth = 10 m

Height = 4. 5 m

We know that

Volume of the cuboid = length x breadth x height cubic units

Substitute the given values in the formula

V = 12 x 10 x 4.5 = 540 m3

Therefore, the volume of a cuboid is 540 m3

ii) To find the volume of a cuboid

Given: Length = 4 m

Breadth = 2.5 m

Height = 50 cm = 0.5 m [since 1 m = 100 cm ]

We know that

Volume of the cuboid = length x breadth x height cubic units

Substitute the given values in the formula

V = 4 x 2.5 x 0.5 = 5 m3

Therefore, the volume of a cuboid is 5 m3

iii) To find the volume of a cuboid

Given: Length = 10 m

Breadth = 2.5 dm

Height = 25 cm = 0. 25 m [since 1 m = 100 cm ]

We know that

Volume of the cuboid = length x breadth x height cubic units

Substitute the given values in the formula

V = 10 x 2.5 x 0.25 = 6.25 m3

Therefore, the volume of a cuboid is 6.25 m3

Q 2. Find the volume in cubic decimeter of each of the cubes whose side is :

i) 1.5 m

ii) 75 cm

iii) 2 dm 5 cm

Soln :

i) Given:Side of the cube, a = 1.5 m

Convert metre into decimeter:

We know that 1 m = 10 dm, so

= 1.5 x 10 dm

a = 15 dm

Volume of the cube = (side)3 Cubic units

Substitute the side value

V =  (  15 )3 = 3375 dm3

Therefore, the volume of a cube is 3375 dm3

ii) Given: Side of the cube, a = 75 cm

Convert metre into decimeter:

We know that 10 m = 1 dm, so

= 75 x (1/10)

a = 7.5 dm

Therefore, Volume of the cube = ( side )3 Cubic units

Substitute the side value

V = ( 7.5 )3 = 421.875 dm3

Therefore, the volume of a cube is 421.875 dm3

iii) Given: Side of the cube,a = 2 dm 5 cm

Convert metre into decimeter:

We know that 1 dm = 10 cm, so

= 2 dm + 5 x \(\frac{ 1 }{ 10 }\) dm

= 2 dm + 0.5 dm = 2.5 dm

Volume of the cube = (side)3 Cubic units

Substitute the side value

V= ( side )3 = ( 2.5 )3 = 15.625 dm3

Therefore, the volume of a cube is 15.625 dm3

Q3. How much clay is dug out in digging a well measuring 3 m by 2 m by 5 m?

Soln:

Given that, the dimension of the well is 3 m x 2 m x 5 m

We know that, the volume of a cuboid = length x breadth x height cubic units

Substitute the dimension value in the formula,

V = ( 3 x 2 x 5 ) m3 = 30 m3

Therefore, the volume of the clay dug out from a well is 30 m3

Q4. What will be the height of cuboid of volume 168 m3, if the area of its base is 28 m2?

Soln:

Given that, Base area of a cuboid =  28 m2

The volume of the cuboid = 168 m3

Let the height of the cuboid be “h”

We know that,

Area of the rectangular base = length x breadth square units

The volume of the cuboid = length x breadth x height cubic units

So, the volume of the cuboid = ( area of the base ) x height

Substitute the given value,

168 = 28 x h

h = 168 / 28 = 6 cm

Hence, the height of the cuboid is 6 m.

Q 5. A tank is 8 m long, 6 m broad and 2 m high. How much water can it contain?

Soln:

Let the length of the cuboidal-shaped tank = 8 m

Breadth = 6 m

Height = 2 m

The volume of a cuboid= length x breadth x height cubic units

Substitute the values

V = ( 8 x 6 x 2 ) m3 = 96 m3

Since 1m3 = 1000 L

Now, 96 m3 = 96 x 1000 L

V = 96000 L

Hence, the cuboidal shaped tank can store 96000 Litres of water.

Q 6. 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.

Soln:

Given that the capacity or the value of the cuboidal tank = 50000 L

We know that 1000 L = 1 m3

It means that,

50000 L = 50 x 1000 litres = 50 m3

So, the volume of the tank is 50 m3.

It is given that,  the length of the tank is 10 m.

Also, it is given that the length of the tank is 10 m.

the height of the tank is 2.5 m.

Let “b” be the breadth of the tank.

so, the volume of the cuboid = length x breadth x height cubic units

Substitute the values,

50 = 10 x b x 2.5

50 = 25 x b

b =50/25 = 2 cm

Hence, the breadth of the tank is 2 m.

Q 7. A rectangular diesel tanker is 2 m long, 2 m wide and 40 cm deep. How many litres of diesel can it hold?

Soln:

Given:

Length, Breadth, and height of the rectangular diesel tanker is 2 m, 2 m, 40 cm respectively.

Since the height is given in cm, convert into the meter.

So, h= 0.4 m [40 x (1/100)]  m

Therefore, the volume of the tanker = length x breadth x height cubic units

Substitute the values,

= 2 x 2 x 0.4 = 1.6 m3

Also, we know that 1 m3 = 1000 L

i.e., 1.6 m3 = 1.6 x 1000 L = 1600 L

Hence, the rectangular diesel tanker can hold 1600 Litres of diesel.

Q8. 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.

Soln:

Given,

Length, breadth, and height of the room is 5 m, 4.5m, 3m respectively.

so, the volume of the cuboid = length x breadth x height cubic units

Substitute the values,

V = 5 x 4. 5 x 3

V = 67. 5 m3

Hence, the volume of air in the room is 67.5 m3.

Q 9. A water tank is 3 m long, 2 m broad and 1 m deep. How many litres of water can it hold?

Soln:

Length, breadth, and height of the water tank is 3 m, 2m, 1m respectively.

so, the volume of the water tank = length x breadth x height cubic units

Volume of the water tank = 3 x 2 x 1= 6 m3

Substitute the values,

Also, we know that 1 m3 = 1000 L

It means that , 6 m3 = 6 x 1000 L = 6000 L

Hence, the water tank can hold 6000 Litres of water.

Q 10. 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?

Soln:

Given that, the length of the wooden block = 6 m = 600 cm [ Since  1 m = 100 cm ]

Breadth of the wooden block = 75 cm

Height of the wooden block = 45 cm

So, the volume of wooden block = length x breadth x height cubic

V= 600 x 75 x 45 = 2025000 cm3

Therefore, the volume of the wooden block, V= 2025000 cm3

Also, given that the length of a plank = 3 m = 300 cm [ Since  1 m = 100 cm ]

Breadth of the plank= 15 cm

Height of the plank= 5 cm

So, the volume of the plank = length x breadth x height cubic units

V = 300 x 15 x 5

= 22500 cm3

Therefore, the volume of the plank  is 22500 cm3

So, the number of planks =volume of the wooden block/ volume of a plank

2025000/ 22500 = 90

Hence, the number of planks is 90.

Q 11. How many bricks will each of size 25 cm x 10 cm x 8 cm 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?

Soln:

Given that the dimension of a brick = 25 cm x 10 cm x 8 cm

So, the volume of a brick = 25 cm x 10 cm x 8 cm = 2000 cm³

Also, given that the length of the wall is 5 m = 500 cm ( since 1 m = 100 cm )

Height of the wall = 3 m = 300cm ( Since 1 m = 100 cm )

The thickness of the wall = 16 cm

i.e., breadth = 16 cm

Therefore, the volume of the wall = length x breadth x height cubic units

V = 500 x 300 x 16 = 2400000 cm3

So, the number of bricks needed to build the wall =  volume of the wall /volume of a brick 

V=  2400000/2000 cm = 1200

Therefore, no.0f. bricks required to build a wall is 1200.

Q 12. 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?

Soln:

Given: Total population of a village =4000

Each person needs 150 L of water a day.

Therefore, the total requirement of water in a day = 4000 x 150 L = 600000 L

It is given that the length of the water tank is 20 m.

The breadth of water tank= 15 m

Height of water tank = 6 m

Therefore, the volume of the tank = length x breadth x height

V= 20 x 15 x 6 = 1800 m3

we know that 1 m3= 1000 L

1800 m3 = 1800 x 1000 L = 1800000 Litres

So. the whole village needs 600000 Litres of water per day in which the tank has 1800000 L of water in it

Hence, the water in the tank will last = 1800000/600000 = 3

Therefore, the water in the tank lasts for 3 days.

Q 13. A rectangular field is 70 m long and 60 m broad. A well of dimensions 14 m x 8 m x 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?

Soln:

Given: The dimension of the well = 14 m x 8m x 6m

So, The volume of the well = 14 x 8 x 6 = 672 m3

When we will spread this dug-out earth on a  rectangular field whose length, breadth is 70 m, and 60 m respectively.

Let h be the height of the rectangular field.

Therefore, the volume of the dug-out earth = length x breadth x height

V = 70 x 60 x h

672 = 4200 x h

h =672/ 4200 = 0.16 m = 16 cm [since 1 m = 100 cm]

Hence, the earth level will rise by 16 cm.

Q 14. A swimming pool is 250 m long and 130 m wide. 3250 cubic meters of water is pumped into it. Find the rise in the level of water.

Soln:

Given that, the length of the swimming pool = 250 m

The breadth of the swimming pool = 130 m

Also. given that the capacity or volume of water in the pool, V is 3250 m3

Let the height of the water level be “h” metres.

Therefore,  the volume of the water = length x breadth x height

Substitute the values in the formula,

3250 = 250 x 130 x h

3250 = 32500 x h

h =  3250 /32500 = 0.1 m

Hence, the level of water in the swimming pool will rise by 0.1 m.

Q 15. A beam 5 m long and 40 cm wide contains 0.6 cubic meters of wood. How thick is the field on that day?

Soln:

Given that, the length of the beam is 5m

The breadth of the beam is 40 cm = 0.4m [Since 100 cm = 1 m]

Let the height of the beam be “h” m.

Also, given that, the volume of the beam, V =  0.6 m3

So, to find the height of the beam, substitute the given value in the formula,

The volume of the cuboidal beam = length x breadth x height

6 = 5 x 0. 4 x h

0.6 = 2 x h

h =0.6/2

h = 0.3

Therefore, the thickness of the beam is 0.3m

Q 16. The rainfall on a certain day was 6 cm. How many litres of water fell on 3 hectares of the field on that day?

Soln:

Given that, the rainfall on a certain day is 6 cm = 0.06m [ since  1 m = 100 cm ]

Also, the area of the field = 3 hectares

W. k.t., 1 hectare = 10000 m2

So, 3 hectares = 3 x 10000 m2 = 30000 m2

Therefore, the volume of rain water that fell in the field = (area of the field ) x ( height of rainfall ) cubic units

V = 30000 x 0.06

V = 1800 m3

Since 1 m3 = 1000 L, We can write it as,

1800 m3 = 1800 x 1000 L = 1800000 L = 18 x 100000 L = 18 x 105 L

Thus,  18 x 105 Litres of rain water fell on the field on that day.

Q 17. An 8 m long cuboidal beam of wood when sliced produces four thousand 1 cm cubes and there are no wastages of wood in this process. If one edge of the beam is 0.5 m, find the third edge.

Soln:

Given that the length of the wooden beam is 8 m

Width of the wooden beam is 0.5 m

Let the height of the wooden beam be “h” m

Therefore, the volume of the wooden cuboidal beam,  its volume = length x width x height cubic units

V = 8 x 0.5 x h

V = 4 x h m3

It is given that, the wooden beam produces 4000 cubes, in which each of edge 1 cm = 1 x 1 m = 0.01 m ( since 100 cm = 1 m )

Therefore, the volume of a cube = (side)3 = (0.01)3 = 0.000001 m3

So, the volume of 4000 cubes = 4000 x 0.000001 = 0.004 m3

Also while preparing the cubes, there is no wastage, the volume of the 4000 cubes will be equal to the volume of the cuboidal beam.

It becomes

The volume of the cuboidal beam = volume of 4000 cubes

Now substitute the obtained values

4 x h = 0.004

h =  0.004 /4 = 0.001 m

Hence, the third edge of the wooden beam is 0.001 m.

Q 18. 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?

Soln:

Given: The dimension of the metal block = 2.25 m x 1.5 m x 27 cm,

i.e. , 225 cm x 150 cm x 27 cm (Since 1 m = 100 cm ).

Therefore, the volume of the metal block = 225 x 150 x 27

Volume of metal block = 911250 cm3

From the given information, the metal block is melted and recast into cubes whose each side is 45 cm.

The volume of a cube = (side) cubic units

The volume of a cube = 453

V= 91125 cm3

So, the number of cubes formed from the metal block = Volume of the metal block / Volume of a metal cube 

911250 /91125

=10

Therefore, 10 cubes are formed from the metal block.

Q 19. A solid rectangular piece of iron measures 6 cm by 6 cm by 2 cm. Find the weight of this piece, if 1 cm3 of iron weighs 8 gm.

Soln:

Given that, the dimensions of the an iron piece = 6 m x 6 cm x 2 cm,

To convert metre into centimeter:

i.e. , 600 cm x 6 cm x 2 cm ( since 1 m = 100 cm ).

Therefore, the volume of a rectangular piece iron = 600 x 6 x 2

V = 7200 cm3

It is given that, 1 cm3 = 8 gm

therefore 7200 cm3 = 7200 x 8 gm = 57600 gm

Thus, the weight of the iron piece = 57600 gm

To covert grams interms of kilogram,

weight= 57600 x  (1/ 1000) kg ( Since 1 Kg = 1000 gm )

Therefore, the weight of the iron piece is 57.6 kg

Q 20. Fill in the blanks in each of the following so as to make the statement true :

i) 1 m3 = ________ cm³

ii) 1 litre = _________ cubic decimeter

iii) 1 kl = _________ m³

iv) the volume of a cube of side 8 cm is ________

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

vi) 1 cu. dm = ________ cu. mm

vii) 1 cu . km = _______ cu . m

viii) 1 litre = ________ cu. cm

ix) 1 ml = _______ cu . cm

x) 1 kl = ________ cu. Dm = ______ cu. cm

Soln:

i)  106 cm3

Explanation:

We know that, 1 m3 = 1m x 1m x 1 m

= 100 cm x 100 cm x 100 cm (since 1 m = 100 cm )

= 1000000 cm3 = 106 cm3

ii) 1 dm3

Explanation:

We know that, 1 L =1 /1000 m3

= ( 1 1000 ) x 1 m x 1 m x 1 m (Since 1 m to 10 dm)

=  (1 / 1000)x 10 dm x 10 dm x 10 dm = 1 dm3

iii) 1 m3

Explanation:

We know that, 1 kL = 1000 L

= 1 m3 ( 1000 L = 1 m3 )

iv) 512 cm3

Explanation:

We know that, Volume of a cube  = side3

Where side, a = 8 cm

V = 83 = 512 cm3

v) 50 cm

Explanation:

Given: Length of the wooden cuboid = 10 cm

Breadth of the wooden cuboid = 8 cm

Its volume of the wooden cuboid = 4000 cm3

Let the height of the cuboid be “h” cm

Then, Volume of the cuboid = length x breadth x height cubic units

Substitute the values

4000 = 10 x 8 x h

4000 = 80 x h

h = 4000/ 80 = 50 cm

vi) 106 cu mm

Explanation:

We know that, 1 cu dm = 1 dm x 1 dm x 1 dm

= 100 mm x 100 mm x 100 mm (since 1 dm = 100 mm)

= 1000000 mm3

= 106 cu mm

vii )109 m3

Explanation:

We know that, 1 cu km = 1 km x 1 km x 1 km

= 1000 m x 1000 m x 1000 m ( w.k.t., 1 km = 1000 m )

= 109 m3

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