## RD Sharma Class 8 Solutions Chapter 21 Mensuration II (Volumes and Surface Areas of a Cubiod and a Cube) Ex 21.1

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 21 Mensuration II Ex 21.1

**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 of a cuboid whose**

**(i) length = 12 cm, breadth = 8 cm, height = 6 cm**

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

**(iii) length = 15 cm, breadth = 2.5 dm, height = 8 cm**

**Solution:**

In a cuboid,

**(i)** Length (l) = 12 cm

Breadth (b) = 8 cm

Height (h) = 6 cm

∴ Volume = Ibh = 12 x 8 x 6 cm^{3} = 576 cm^{3}

**(ii)** Length (l) = 1.2 m = 120 cm

breadth (6) = 30 cm

Height (h) = 15 cm

∴ Volume = Ibh = 120 x 30 x 15 cm^{3} = 54000 cm^{3}

**(iii)** Length (l) = 15 cm

Breadth (b) = 2.5 dm = 25 cm

Height (h) = 8 cm

∴ Volume = Ibh

= 15 x 25 x 8 cm^{3} = 3000 cm^{2}

**Question 2.**

**Find the volume of the cube whose side is**

**(i) 4 cm**

**(ii) 8 cm**

**(iii) 1.5 dm**

**(iv) 1.2 m**

**(v) 25 mm.**

**Solution:**

**(i)** Side of a cube (a) = 4 cm

∴ Volume = a3 = (4)^{3} cm^{3} = 4 x 4 x 4 = 64 cm^{3}

**(ii)** Side of cube (a) = 8 cm

∴ Volume = a3 = (8)^{3} 4 cm

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

**(iii)** Side of cube (a) = 1.5 dm = 15 cm

∴ Volume = a^{3} = (1.5)3 dm^{2} = (15)^{3} cm^{3}

= 15 x 15 x 15 = 3375 cm^{3}

**(iv)** Side of cube (a) = 1.2 m = 120 cm

∴ Volume = a^{3} = (120)^{3} cm^{3}

= 120 x 120 x 120 = 1728000 cm^{3}

**(v)** Side of cube (a) = 25 mm = 2.5 cm.

∴ Volume = a^{3} = (2.5)^{3} cm^{3}

= 2.5 x 2.5 x 2.5 cm^{3} = 15.625 cm^{3}

**Question 3.**

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

**Solution:**

Volume of a cuboid =100 cm^{3}

Length (1) = 5 cm

and breadth (b) = 4 cm

**Question 4.**

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

**Solution:**

Volume of the liquid in the vessel = 300 cm^{3}

Length (l)= 10 cm

Breadth (b) = 5 cm

**Question 5.**

**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 ?**

**Solution:**

Capacity of milk = 4 litres

∴ Volume of the container = 4 x 1000 cm^{3} = 4000 cm^{3}

Length (l) = 8 cm

Width (b) = 50 cm

**Question 6.**

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

**Solution:**

Volume of wooden cuboid block = 36 cm

^{3}

Length (l) = 4 cm

Breadth (b) = 3 cm

**Question 7.**

**What will happen to the volume of a cube, if its edge is (i) halved (ii) trebled ?**

**Solution:**

Let side of original cube = a cm

∴ Volume = a^{3} cm^{3}

(i) In first case,

(ii) In second case, when side (edge) is trebled, then side = 3a

∴ Volume = (3a)^{3} = 27a^{3}

∴ It will be 27 times

**Question 8.**

**What will happen to the volume of a 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:**

Let l, b and h be the length, breadth and height of the given cuboid respectively.

∴ Volume = lbh.

**(i)** Length is doubled = 21

∴ The volume will be the same.

**(ii)** Length is doubled = 21

breadth is same = b height is doubled = 2h

∴ Volume = 2l x b x 2h = 4 lbh

∴ Volume will be 4 times

**Question 9.**

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

**Solution:**

Dimensions of first cuboid = 5 cm x 6 cm x 7 cm

∴ Volume = 5 x 6 x 7 = 210 cm^{3}

Dimensions of second cuboid = 4 cm x 7 cm x 8 cm

∴ Volume = 4x 7 x 8 = 224 cm^{3}

Dimensions of third cuboid = 2 cm x 3 cm x 13 cm

∴ Volume = 2 x 3 x 13 = 78 cm^{3}

Total volume of three cubes = 210 + 224 + 78 cm3 = 512 cm^{3}

∴ Volume of cube = 512 cm^{3}

**Question 10.**

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

**Solution:**

Dimension of cuboidal iron piece = 50 cm x 40 cm x 10 cm

∴ Volume = 50 x 40 x 10 = 20000 cm^{3}

Weight of 1 cm^{3} = 8 gm

∴ Total weight of piece = 20000 x 8 gm

**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:**

Length of log (l) = 3 m = 300 cm.

Breadth (b) = 75 cm

and height (h) = 50 cm

∴ Volume of log = lbh = 300 x 75 x 50 cm3 = 1125000 cm^{3}

Side of cubical block = 25 cm

∴ Volume of one block = a^{2} = 25 x 25 x 25 cm3 = 15625 cm^{3}

∴ Number of blocks to be cut out

**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 cm ^{2} each are to be made. Find the number of beads that can be made from the block ?**

**Solution:**

Length of block (l) = 9 cm

Breadth (b) = 4 cm

and height (h) = 3.5 cm

∴ Volume = l x b x h = 9 x 4 x 3.5 cm

^{3}= 126 cm

^{3}

Volume of one bead = 1.5 cm

^{3}

∴ Number of beads = \(\frac { 126 }{ 105 }\) = 84

**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:**

Length of cuboidal box (l) = 2 cm

breadth (b) = 3 cm

and height (h) = 10 cm

∴ Volume = lx b x h = 2 x 3 x 10 = 60 cm^{3}

Volume of carton = 40 x 36 x 24 cm^{3}

= 34560 cm^{3}

∴ Number of boxes to be height in the carton

**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 the block ? Assume cutting causes no wastage.**

**Solution:**

Dimensions of block = 50 cm, 45 cm, 34 cm

∴ Volume = 50 x 45 x 34 = 76500 cm^{3}

Size of cuboid = 5 cm x 3 cm x 2 cm

∴ Volume of cuboid = 5 x 3 x 2 = 30 cm^{3}

**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:**

Let side of cube B = a

Then Volume = a^{3}

and side of cube A = 3a

Volume = (3a)^{3} = 3a x 3a x 2a = 27a^{3}

∴ Ratio of volume’s A and B = 27a^{3} : a^{3}

= 27 : 1

**Question 16.**

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

**Solution:**

Dimensions of ice cream brick = 20 cm x 10 cm x 7 cm

∴ Volume = 20 x 10 x 7 cm^{3} = 1400 cm^{3}

Dimensions of inner of fridge = 100 cm x 50 cm x 42 cm = 210000 cm^{3}

∴ Number of bricks to be kept in the fridge

**Question 17.**

**Suppose that there are two cubes, having edges 2 cm and 4 cm, respectively. Find the volume V _{1} and V_{2} of the cubes and compare them.**

**Solution:**

Side of first cube (a) = 2 cm

∴ Volume (V

_{1}) = a

^{3}= (2) = 8 cm

^{3}

Similarly side of second cube = 4 cm

and volume (V

_{2}) = (4)

^{3}= 64 cm

^{3}

Now V

_{2}= 64 cm

^{3}= 8 x 8 cm

^{3}

= 8 x V

_{1}

⇒ V

_{2}= 8V

_{1}

**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:**

Dimensions of tea-packet = 10cm x 6cm x 4 cm

∴ Volume =10 x 6 x 4 = 240 cm^{3}

Dimensions of box = 50 cm x 30 cm x 0.2 m

= 50 cm x30 cm x20 cm

∴ Volume = 50 x 30 x 20 = 30000 cm^{3}

∴ Number of tea-packets to be kept = \(\frac { 30000 }{ 240 }\)

**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:**

Dimensions of a metal block = 5 cm x 4 cm x 3 cm = 5 x 4 x 3 = 60 cm^{3}

Dimensions of a second block = 15 cm x 8 cm x 3 cm = 15 x 8 x 3 = 360 cm^{3}

But weight of first block = 1 kg

∴ Weight of second block

= \(\frac { 1 }{ 16 }\) x 360 = 6 kg

**Question 20.**

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

**Solution:**

Size of box = 56 cm x 0.4 m x 0.25 m = 56 cm x 40 cm x 25 cm

∴ Volume = 56 x 40 x 25 cm^{3} = 56000 cm^{3}

Size of a soap cake = 7 cm x 5 cm x 2.5 cm

∴ Volume = 7 x 5 x 2.5 cm^{3} = 87.5 cm^{3}

∴ Number of cakes to be kept in the box

= \(\frac { 56000 }{ 87.5 }\) = 640

**Question 21.**

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

**Solution:**

Volume of cuboid box = 48 cm^{3}

Length (l) = 4 cm

Height = (h) = 3 cm

Hope given RD Sharma Class 8 Solutions Chapter 21 Mensuration II Ex 21.1 are helpful to complete your math homework.

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