## RD Sharma Class 8 Solutions Chapter 21 Mensuration II Ex 21.2

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 21 Mensuration II Ex 21.2

**Other Exercises**

- RD Sharma Class 8 Solutions Chapter 21 Mensuration II Ex 21.1
- RD Sharma Class 8 Solutions Chapter 21 Mensuration II Ex 21.2
- RD Sharma Class 8 Solutions Chapter 21 Mensuration II Ex 21.3
- RD Sharma Class 8 Solutions Chapter 21 Mensuration II Ex 21.4

**Question 1.**

**Find the volume in cubic metres (cu.m) of each of the cuboids whose dimensions are :**

**(i) length = 12 cm, 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.
**

**Solution:**

**(i)**Length of cuboid (l) = 12 m

Breadth (b) = 10m

and height (h) = 4.5 m

∴Volume = l x b x h = 12 x 10 x 4.5 m

^{3}

= 540 m

^{3}

**(ii)**Length of cuboid (l) = 4 m

Breadth (b) = 2.5m

Height (h) = 50 cm = 0.5 m

∴ Volume = l x b x h = 4 x 2.5 x 0.5 = 5 m

^{3}

**(iii)**Length of cuboid (l) = 10 m

Breadth (b) = 25 dm = 2.5 m

Height (h) = 25 cm 0.25 m

∴ Volume = l x b x h = 10 x 2.5 x 0.25 m

^{3}= 6.25 m

^{3}

**Question 2.**

**Find the volume in cubic decimetre of each of the cubes whose side is**

**(i) 1.5 m**

**(it) 75 cm**

**(iii) 2 dm 5 cm**

**Solution:**

**(i)** Side of cube (a) = 1.5 m

∴ Volume = a^{3} = (1.5)^{3} m^{3}

= 1.5 x 1.5 x 1.5 m^{3} = 3.375 m^{3}

= 3.375 x 1000 = 3375 dm^{3}

**(ii)** Side of cube (a) = 75 cm = 7.5 dm

∴ Volume = a^{3} = (7.5)3 dm^{3}

= 421.875 dm^{3}

**(iii)** Side of cube (a) = 2 dm 5 cm = 2.5 dm

∴ Volume = (a)^{3} = (2.5)^{3} dm^{3}

= 15.625 dm^{3}

**Question 3.**

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

**Solution:**

Length of well (l) = 3m

breadth (b) = 2 m

and height (depth) (h) = 5 m

Volume of earth dug out = l x b x h = 3 x 2 x 5 = 30m^{3}

**Question 4.**

**What will be the height of a cuboid of volume 168 m ^{3}, if the area of its base is 28 m^{2} ?**

**Solution:**

Volume of a cuboid = 168 m

^{3}

Area of its base l.e., l x b = 28 m

^{3}

**Question 5.**

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

**Solution:**

Length of tank (l) = 8 m

Breadth (b) = 6 m

Height (h) = 2 m

∴ Volume of water in the tank = l x b x h = 8 x 6 x 2 = 96 m^{3}

= 96 x 1000 = 96000litres (∵1m^{3} = 1000litre)

**Question 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.**

**Solution:**

Capacity of water in the tank = 50000 litres

∴ Volume of water = 50000 x \(\frac { 1 }{ 1000 }\) = 50 m^{3} (1000 l = 1 m^{3})

Height of tank (h)= 10 m

and length (l) = 2.5 m

Volume 50

**Question 7.**

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

**Solution:**

Length of tanker (l) = 2 m

Breadth (b) = 2m

Depth (h) = 40 cm = 0.4 m

∴ Volume = l x bx h = 2 x 2 x 0.4=1.6m^{3}

Quantity of diesel = 1.6 x 1000 litres (1 m^{3}= 1000 l)

= 1600 litres

**Question 8.**

**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.**

**Solution:**

Length of room (l) = 5 m

Breadth (6) = 4.5 m

and height (h) = 3 m

∴ Volume of air it contains

= l x b x h = 5 x 4.5 x 3 m^{3}

= 67.5 m^{3}

**Question 9.**

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

**Solution:**

Length of tank (l) = 3 m

Breadth (b) = 2 m

and depth (h) = 1 m

∴ Volume of tank = l x b x h

= 3 x 2 x 1 = 6 m^{3}

∴ Quantity of water it can contains

= 6 x 1000 litres = 6000 litres (1 m^{3}= 1000 litres)

**Question 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 ?**

**Solution:**

Length of wooden block (l) = 6 m

Width (b) = 75 cm = 0.75 m

Thickness (h) = 45 cm = 0.45 m

∴ Volume = l x b x h = 6 x 0.75 x 0.45 m^{3}

Length of plank (l) = 3 m

Breadth (b) = 15 cm = 0.15 m

Thickness (h) = 5 cm = 0.05 m

∴ Volume = 3 x 0.15 x 0.05 m^{3}

Number of planks

**Question 11.**

**How many bricks each of size 25 cm x 10 cm x 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 ?**

**Solution:**

Size of one brick = 25 cm x 10 cm x 8 cm

∴ Volume of one brick = 25 x 10 x 8 cm^{3}

Length of wall (l) = 5 m

Width (b) = 0.16 m

Height (h) = 3 m

∴ Volume of wall = l x b x h

= 5 x 0.16 x 3 m^{3} = 2.4 m^{3}

∴ Number of bricks required

**Question 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 the water of this tank will last ?**

**Solution:**

Total population of a village = 4000

Water required for each person for one day = 150 litres

∴ Water required for 4000 persons for one day = 150 x 4000 = 600000 litres

Length of tank (l) = 20 m

Breadth (b) = 15 m

Height (h) = 6 m

∴ Volume of tank = l x b x h = 20 x 15 x 6 m^{3} = 1800 m^{3}

Capacity of water in the tank = 1800 x 1000 l= 1800000l (1 m^{3} = 1000 l)

∴ Number of days, the water will last

**Question 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 dugout from this well is spread evenly on the field. How much will the earth level rise ?**

**Solution:**

Length of well (l) = 14 m

Breadth (A) = 8m

Depth (A) = 6m

∴ Volume of earth dugout = l x bx h

= 14 x 8 x 6 = 672 m^{3} Length of field = 70 m

and breadth = 60 m

Let h be the height of earth spread over

Then 70 x 60 x h = 672

⇒ h = \(\frac { 672 }{ 70×60 }\) = 0.16m

∴ Height of earth = 0.16 m = 16 cm

**Question 14.**

**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.**

**Solution:**

Volume of water = 3250 m^{3}

Length of pool (l) = 250 m

Breadth (b)= 130 m

∴ Height of water level

**Question 15.**

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

**Solution:**

Volume of wood of the beam = 0.6 m^{3} = 600000

Length of beam (l) = 5 m = 500 cm

Breadth (b) = 40 cm

**Question 16.**

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

**Solution:**

Area of the field = 3 hectares

= 3 x 10000 square metres

= 30000 square metres

Height of rainfall = 6 cm = m^{3}

**Question 17.**

**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.**

**Solution:**

Length of cuboidal beam (l) = 8 m = 800 cm

Number of cubical sliced = 4000

Edge of each cube = 1 cm

Volume of beam = 4000 (1)^{3} cm^{3} = 4000 cm^{3}

One edge of the beam = 0.5 m = 50 cm.

**Question 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 ?**

**Solution:**

Dimensions of metal block = 2.25 m x 1.5 m x 27 cm

∴ Volume = 2.25 x 1.5 x 0.27 m^{3}

= 225 x 150 x 27 cm^{3} = 911250 cm^{3}

Side of each cube (a) = 45 cm

∴ Volume of one cube = a^{3} = (45)^{3} cm^{3} = 91125 cm^{3}

∴ Number of cubes = \(\frac { 911250 }{ 91125 }\) = 10

**Question 19.**

**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.**

**Solution:**

Dimensions of a piece of rectangular iron = 6m x 6cm x 2cm

∴ Volume = 600 x 6 x 2 cm^{3} = 7200 cm^{3}

Weight of 1 cm^{3} = 8 gm

∴ Total weight of the piece = 7200 x 8 gm

= 57600 gm = \(\frac { 57600 }{ 1000 }\) kg = 57.6 kg

**Question 20.**

**Fill in the blanks in each of the following so as to make the statement true :**

**(i) 1 m ^{3} = ……… cm^{3}**

**(ii) 1 litre = …….. cubic decimetre**

**(iii) 1 kl = …… m**

^{3}**(iv) The volume of a cube of side 8 cm is …….. .**

**(v) The volume of 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.**

**Solution:**

**(i)**1 m

^{3}= 1000000 or

**10**

^{6 }cm^{3}**(ii)**1 litre =

**1**cubic decimetre

**(iii)**1 kl =

**1**m

^{3}

**(iv)**The volume of a cube of side 8 cm is

**512 cm**(V = a

^{3}^{3}= 8 x 8 x 8 = 512 cm

^{3})

**(v)**The volume of a wooden cuboid of length 10 cm and breadth 8 cm is 4000 cm

^{3}. The height of the cuboid is

**50 cm**

**(vi)**1 cu.dm =

**1000000**cu mm =

**10**

^{6}cu.mm**(vii)**1 cu.km =

**1000 x 1000 x 1000 cu.m**= 109 cu.m

**(viii)**1 litre =

**1000 cu.cm = 10**cu.cm

^{3}**(ix)**1 ml = 1 cu.cm

**(x)**1 kl =

**1000**cu.dm =

**100 x 100 x 100 cu.cm = 10**cu.cm

^{6}Hope given RD Sharma Class 8 Solutions Chapter 21 Mensuration II Ex 21.2 are helpful to complete your math homework.

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