Class 8 RD Sharma Solutions - Chapter 21 Mensuration II (Volume and Surface Areas of a Cuboid and a Cube) - Exercise 21.1 | Set 2

Chapter 21 Mensuration II (Volume and Surface Areas of a Cuboid and a Cube) - Exercise 21.1 | Set 1

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: 

The details given about cuboidal block of silver are -

Length of cuboidal block = 9 cm

Breadth of cuboidal block = 4 cm

Height of cuboidal block = 3.5 cm

Volume of a cuboid = l * b * h

                                = 9 * 4 * 3.5

                                = 126 cm³

Number of beads = Volume of cuboid / Volume of bead

                             = 126 / 1.5

                             = 84 beads

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: 

The details given about cuboidal boxes are -

Length of cuboidal boxes = 2 cm

Breadth of cuboidal boxes = 3 cm

Height of cuboidal boxes = 10 cm

Volume of a cuboid = l * b * h

                                = 2 * 3 * 10

                                = 60 cm³

The details given about cartoon are -

Length of cartoon = 40 cm

Breadth of cartoon = 36 cm

Height of cartoon = 24 cm

Volume of a cartoon = l * b * h

                                  = 40 * 36 * 24

                                  = 34560 cm³

Number of boxes that can be stored in a cartoon = Volume of cartoon / Volume of cuboid

                                                                                = 34560 / 60

                                                                                = 576 boxes

Question 14: A cuboidal block of solid iron has dimension 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: 

The details given about cuboidal block are -

Length of cuboidal block = 50 cm

Breadth of cuboidal block = 45 cm

Height of cuboidal block = 34 cm

Volume of a cuboid = l * b * h

                                = 50 * 45 * 34

                                = 76500 cm³

The details given about cuboid are -

Length of cuboid = 5 cm

Breadth of cuboid = 3 cm

Height of cuboid = 2 cm

Volume of a cuboid = l * b * h

                                = 5 * 3 * 2

                                = 30 cm³

Number of boxes that can be stored in a cartoon = Volume of cartoon / Volume of cuboid

                                                                             = 76500 / 30

                                                                             = 2550 cuboids

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 = x

Now side of cube A = 3x

Volume of cube A = (side)³

                             = (3x)³

                                       = 27x³

Volume of cube B = (side)³

                             = (x)³

                             = x³

Volume of cube A / Volume of cube B = 27x³ / x³

                                                           = 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: 

The details given about ice - cream brick are -

Length of ice - cream brick  = 20 cm

Breadth of ice - cream brick = 10 cm

Height of ice - cream brick = 7 cm

Volume of a ice - cream brick = l * b * h

                                                = 20 * 10 * 7

                                                = 1400 cm³

The details given about fridge are -

Length of fridge = 100 cm

Breadth of fridge = 50 cm

Height of fridge = 42 cm

Volume of a fridge = l * b * h

                               = 10 * 50 * 42

                               = 21000 cm³

Number of brick that can be stored in fridge = Volume of fridge / Volume of brick

                                                                        = 21000 / 14000

                                                                        = 150 bricks

Question 17: Suppose that there are two cubes, having edges 2 cm and 4 cm, respectively. Find the volumes V₁ and V₂ of the cubes and compare them.

Solution: 

Volume of cube = (side)³

 V₁ = (2)³

       = 8 cm³

Volume of cube = (side)³

                     V₂ = (4)³

                         = 64

V₁ / V₂ = 8 / 64

V₁ / V_{2 =} 1 / 8

V₂ = 8V₁

Question 18: 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?

Solution:  

The details given about tea - packet are -

Length of tea - packet  = 10 cm

Breadth of tea - packet = 6 cm

Height of tea - packet = 4 cm

Volume of a tea - packet = l * b * h

                                        = 10 * 6 * 4

                                        = 240 cm³

The details given about cardboard box are -

Length of cardboard box = 50 cm

Breadth of cardboard = 30 cm

Height of cardboard = 0.2 m = 20 cm (1 m = 100 cm)

Volume of a cardboard box = l * b * h

                                           = 50 * 30 * 20

                                           = 30000 cm³

Number of tea - packets that can be placed in cardboard box = Volume of cardboard box / Volume of tea packet

                                                                                                 = 30000 / 240

                                                                                                 = 125 tea packet

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 details given metal block are -

Length of block  = 5 cm

Breadth of block = 4 cm

Height of block = 3 cm

Volume of block = l * b * h

                          = 5 * 4 * 3

                          = 60 cm³

The details given about new box are -

Length of new block  = 15 cm

Breadth of new block = 8 cm

Height of new block = 3 cm

Volume of new block = l * b * h

                                  = 15 * 8 * 3

                                  = 360 cm³

Weight of 60 cm³ block = 1 kg 

Weight of 360 cm³ block = 360 / 60

                                       = 6 kg

Question 20: 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?

Solution: 

The details given about box are -

Length of box  = 56 cm

Breadth of box = 0.4 m = 40 cm (1 m = 100 cm)

Height of box = 0.25 m = 25 cm (1m = 100 cm)

Volume of a box = l * b * h

                           = 56 * 40 * 25

                           = 56000 cm³

The details given about soap cake are -

Length of soap cake = 7 cm

Breadth of soap cake = 5 cm

Height of soap cake = 2.5 cm

Volume of a soap cake = l * b * h

                                    = 7 * 5 * 2.5

                                    = 87.5 cm³

Number of soap cakes that can be placed in a box = Volume of cardboard box / Volume of soap cake

                                                                               = 56000 / 87.5

                                                                               = 640 soap cakes

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: 

The details given about cuboidal box are

Volume of a cuboidal box = 48 cm³

Height of a cuboidal box = 3 cm

Length of a cuboidal box = 4 cm

Let height of cuboidal box = h

Volume of cuboid = l * b * h

                       48 = 3 * 4 * h

                      48 = 12 * h

                       h = 4 cm