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Class 8 RD Sharma Solutions – Chapter 21 Mensuration II (Volumes and Surface Areas of a Cuboid and a Cube) – Exercise 21.1 | Set 1

  • Last Updated : 16 Apr, 2021

Question 1: Find the volume of cuboid whose:

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

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

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



Solution:

 i) The details given about cuboid are –

Length of cuboid = 12 cm

Breadth of cuboid = 8 cm

Height of cuboid = 6 cm

Volume of cuboid = length * breadth * height

                              = 12 * 8 * 6

                              = 576 cm3



ii) The details given about cuboid are-

      Length of cuboid = 1.2 m = 120 cm (1 m = 100 cm)

      Breadth of cuboid = 30 cm

      Height of cuboid = 15 cm

      Volume of cuboid = length * breadth * height

                                    = 120 * 30 * 15

                                     = 54000 cm3

iii) The details given about cuboid are –

     Length of cuboid = 1.5 dm = 15 cm (1 dm = 10 cm)

     Breadth of cuboid = 2.5 dm = 25 cm (1dm = 10 cm)



     Height of cuboid = 8 cm

     Volume of cuboid = length * breadth * height

                                  = 15 * 25 * 8

                                  = 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 details given about cube are:

Side of cube = 4 cm   

Volume of cube = (side)3

                          = (4)3

                          = 64 cm3

ii) The details given about cube are:

     Side of cube = 8 cm  

     Volume of cube = (side)3

                               = (8)3

                               = 512 cm3



iii) The details given about cube are:

       Side of cube = 1.5 dm = 15 cm (1 dm = 10 cm)

       Volume of cube = (side)3

                              = (15)3

                              = 3375 cm3

iv) The details given about cube are –

      Side of cube = 1.2 m = 120 cm (1 m = 100 cm)

      Volume of cube = (side)3

                             = (120)3

                             = 1728000 cm3

v) The details given about cube are –

      Side of cube = 25 mm = 25 * 0.1 = 2.5 cm 

      Volume of cube = (side)3

                                = (2.5)3

                                = 15.625 cm3

Question 3: Find the height of a cuboid of volume 100 cm3, whose length and breadth are 5cm and 4cm respectively.

Solution: 

The details given about cuboid are –

Volume of cuboid = 100cm3

Length of cuboid = 5 cm

Breadth of cuboid = 4 cm



Let height of cuboid = h

Volume of cuboid = l * b * h   

100 = 5 * 4 * h

100 / 20 = h

5cm = h   

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: 

The details given about cuboid vessel are –

Volume of cuboid vessel = 300cm3

Length of cuboid vessel = 10 cm

Breadth of cuboid vessel = 5 cm

Let height of cuboid vessel = h

Volume of cuboidal vessel = l * b * h  

300 = 10 * 5 * h

300 / 50 = h

6 cm = 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: 

The details given about milk container are –

Volume of milk container = 4 l = 4000 cm3 (1 l = 1000cm3)

Length of milk container = 8 cm

Breadth of milk container = 50 cm

Let height of milk container = h

Volume of milk container = l * b * h  

4000 = 8 * 50 * h

4000 / 400 = h

10 cm = h   

Question 6: A cuboidal wooden block contains 36 cm3 wood. If it be 4 cm long and 3 cm wide. Find its height.

Solution: 

The details given about milk container are –

Volume of wooden block = 36 cm3 

Length of milk container = 4 cm

Breadth of milk container = 3 cm

Let height of milk container = h

Volume of milk container = l * b * h  

36 = 4 * 3 * h

36 / 12 = h

3 cm = h   

Question 7: What will happen if to the volume of cube, if its edge is: 

i) Halved

ii) Trebled

Solution: 

i) Let the side of the cube = x

Volume of cube = (side)3



                                  = x3

When edge is halved,

Volume of cube = (x / 2)3

                                   = x3 / 8

Hence, it means that when edge is halved then volume becomes 1 / 8 times of initial volume.

ii) Let the side of the cube = x

Volume of cube = (side)3

                          = x3

When edge is trebled,

Volume of cube = (3x)3

                          = 27x3

Hence, it means that when edge is trebled then volume becomes 27 times of initial volume.

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:

i) Let length of cuboid = l

Let breadth of cuboid = b

Let height of cuboid = h

Volume of cuboid = l * b * h

                             = lbh

When, 

length = 2l

height = h

breadth = b / 2

Volume of cuboid = 2 * l * b * h / 2

                             = lbh

Hence, if length is doubled. Height is same and breadth is halved then it does not affect initial volume.

ii) Let length of cuboid = l

Let breadth of cuboid = b

Let height of cuboid = h

Volume of cuboid = l * b * h

                             = lbh

When,

Length = 2l

Height = 2h

Breadth = b 

Volume of cuboid = 2 * l * 2 * b * h

                             = 4lbh

Hence, if length is doubled. Height is doubled and breadth then volume becomes 4 times of the initial volume.

Question 9: Three cuboids of the dimension 5 cm * 6 cm * 7 cm , 4 cm * 7 cm * 8 cm and 2 cm * 3 cm * 13 cm are melted and a cube is made. Find the side of the cube.

Solution: 



Volume of first cuboid = 5 * 6 * 7 = 210 cm3

Volume of second cuboid = 4 * 7 * 8 = 224 cm3

Volume of third cuboid = 2 * 3 * 13 = 78 cm3

Volume of cube = Volume of first cuboid + Volume of second cuboid + Volume of third cuboid 

                         = 210 + 224 + 78

                         = 512 cm3

Volume of cube = (side)3

512 = (side)3  

8 cm = side

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

Solution: 

The details given about solid rectangular iron piece are –

Length of solid rectangular iron piece = 50 cm

Breadth of solid rectangular iron piece = 40 cm

Height of solid rectangular iron piece = 10 cm

Volume of solid rectangular iron piece = l * b * h

                                                             = 50 * 40 * 10

                                                             = 20000 cm3

Weight of 1 cm3 of iron = 8 gm

Weight of 20000 cm3 of iron = 20000 * 8 

                                                             160000 gm 

                                             = 160 kg (1 kg = 1000 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: 

The details given about log of wood are –

Length of log of wood = 3 m = 300 cm (1 m = 100 cm)

Breadth of log of wood = 75 cm

Height of log of wood = 50 cm

Volume of log of wood = l * b * h

                                     = 300 * 75 * 50

                                     = 1125000 cm3

Volume of cubical block = (side)3 

                                      = (25)3

                                      = 15625 cm3

Number of cubical blocks = Volume of log of wood / Volume of cubical block

                                        = 1125000 / 15625

                                        = 72 blocks                      

Chapter 21 Mensuration II (Volume and Surface Areas of a Cuboid and a Cube) – Exercise 21.1 | Set 2




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