##### Class 8^{th} Mathematics AP Board Solution

**Exercise 14.1**- There are two cuboidal boxes as shown in the given figure. Which box requires…
- Find the side of a cube whose surface area is 600 cm^2 .
- Prameela painted the outer surface of a cabinet of measures 1m × 2m × 1.5m.…
- Find the cost of painting a cuboid of dimensions 20cm × 15 cm × 12 cm at the…

**Exercise 14.2**- Find the volume of the cuboid whose dimensions are given below.
- Find the capacity of the tanks with the following internal dimensions. Express…
- What will happen to the volume of a cube if the length of its edge is reduced…
- Find the volume of each of the cube whose sides are. (i) 6.4 cm (ii) 1.3 m…
- How many bricks will be required to build a wall of 8 m long, 6m height and…
- A cuboid is 25 cm long, 15 cm broad, and 8 cm high. How much of its volume will…
- A closed box is made up of wood which is 1cm thick. The outer dimensions of the…
- How many cubes of edge 4cm, each can be cut out from cuboid whose length,…
- How many cuboids of size 4 cm × 3 cm × 2 cm can be made from a cuboid of size…
- A vessel in the shape of a cuboid is 30 cm long and 25 cm wide. What should be…

**Exercise 14.1**

- There are two cuboidal boxes as shown in the given figure. Which box requires…
- Find the side of a cube whose surface area is 600 cm^2 .
- Prameela painted the outer surface of a cabinet of measures 1m × 2m × 1.5m.…
- Find the cost of painting a cuboid of dimensions 20cm × 15 cm × 12 cm at the…

**Exercise 14.2**

- Find the volume of the cuboid whose dimensions are given below.
- Find the capacity of the tanks with the following internal dimensions. Express…
- What will happen to the volume of a cube if the length of its edge is reduced…
- Find the volume of each of the cube whose sides are. (i) 6.4 cm (ii) 1.3 m…
- How many bricks will be required to build a wall of 8 m long, 6m height and…
- A cuboid is 25 cm long, 15 cm broad, and 8 cm high. How much of its volume will…
- A closed box is made up of wood which is 1cm thick. The outer dimensions of the…
- How many cubes of edge 4cm, each can be cut out from cuboid whose length,…
- How many cuboids of size 4 cm × 3 cm × 2 cm can be made from a cuboid of size…
- A vessel in the shape of a cuboid is 30 cm long and 25 cm wide. What should be…

###### Exercise 14.1

**Question 1.**There are two cuboidal boxes as shown in the given figure. Which box requires the less amount of material to make?

**Answer:**Measurement of box 1

Length = 60 cm,

Breadth = 40 cm and,

Height = 50 cm

Volume of cuboid = Length × Breadth × Height

= 60 × 40 × 20

= 12000 cm^{3}

Measurement of box 2

Side = 50cm

Volume of cube = (side)^{3}

= (50)^{3}

= 50 × 50 × 50

= 125000 cm^{3}

Box 1 requires less amount of material.

**Question 2.**Find the side of a cube whose surface area is 600 cm^{2}.

**Answer:**Let the side be S.

∴ surface area of cube = 6× side^{2}

⇒ 600 = 6 × s^{2}

⇒ = s^{2}

⇒ s^{2} = 100

⇒ s = √100

⇒ s = 10 cm

**Question 3.**Prameela painted the outer surface of a cabinet of measures 1m × 2m × 1.5m. Find the surface area she cover if she painted all except the bottom of the cabinet?

**Answer:**Measurement of the cuboid

Length(L) = 1 m breadth(B) = 2 m and height(H) = 1.5 m

Total surface area = 2(LB + BH + LH)

= 2(1 × 2 + 2 × 1.5 + 1 × 1.5)

= 2(2 + 3 + 1.5)

= 2(6.5)

= 13 cm^{2}

Area of bottom surface = 1 × 2 = 2m^{2}

Hence, area covered by painting = 13 – 2 = 11 m^{2}

**Question 4.**Find the cost of painting a cuboid of dimensions 20cm × 15 cm × 12 cm at the rate of 5 paisa per square centimeter.

**Answer:**Measurement of the cuboid

Length(L) = 20 cm breadth(B) = 15 cm and height(H) = 12cm

Total surface area = 2(LB + BH + LH)

= 2(20 × 15 + 15 × 12 + 20 × 12)

= 2(300 + 180 + 240)

= 2(720)

= 1440 cm^{2}

Rate of painting 1cm^{2} = ₹0.05

Rate of painting a whole cuboid = 0.05 × 1440

= ₹72

**Question 1.**

There are two cuboidal boxes as shown in the given figure. Which box requires the less amount of material to make?

**Answer:**

Measurement of box 1

Length = 60 cm,

Breadth = 40 cm and,

Height = 50 cm

Volume of cuboid = Length × Breadth × Height

= 60 × 40 × 20

= 12000 cm^{3}

Measurement of box 2

Side = 50cm

Volume of cube = (side)^{3}

= (50)^{3}

= 50 × 50 × 50

= 125000 cm^{3}

Box 1 requires less amount of material.

**Question 2.**

Find the side of a cube whose surface area is 600 cm^{2}.

**Answer:**

Let the side be S.

∴ surface area of cube = 6× side^{2}

⇒ 600 = 6 × s^{2}

⇒ = s^{2}

⇒ s^{2} = 100

⇒ s = √100

⇒ s = 10 cm

**Question 3.**

Prameela painted the outer surface of a cabinet of measures 1m × 2m × 1.5m. Find the surface area she cover if she painted all except the bottom of the cabinet?

**Answer:**

Measurement of the cuboid

Length(L) = 1 m breadth(B) = 2 m and height(H) = 1.5 m

Total surface area = 2(LB + BH + LH)

= 2(1 × 2 + 2 × 1.5 + 1 × 1.5)

= 2(2 + 3 + 1.5)

= 2(6.5)

= 13 cm^{2}

Area of bottom surface = 1 × 2 = 2m^{2}

Hence, area covered by painting = 13 – 2 = 11 m^{2}

**Question 4.**

Find the cost of painting a cuboid of dimensions 20cm × 15 cm × 12 cm at the rate of 5 paisa per square centimeter.

**Answer:**

Measurement of the cuboid

Length(L) = 20 cm breadth(B) = 15 cm and height(H) = 12cm

Total surface area = 2(LB + BH + LH)

= 2(20 × 15 + 15 × 12 + 20 × 12)

= 2(300 + 180 + 240)

= 2(720)

= 1440 cm^{2}

Rate of painting 1cm^{2} = ₹0.05

Rate of painting a whole cuboid = 0.05 × 1440

= ₹72

###### Exercise 14.2

**Question 1.**Find the volume of the cuboid whose dimensions are given below.

**Answer:**i: Length = 8.2 m Breadth = 5.3m and Height = 2.6m

Volume of cuboid = Length × Breadth × Height

= 8.2 × 5.3 × 2.6

= 112.996 m^{3}

ii: Length = 5.0 m Breadth = 4.0m and Height = 3.5m

Volume of cuboid = Length × Breadth × Height

= 5 × 4 × 3.5

= 70 m^{3}

iii: Length = 4.5 m Breadth = 2m and Height = 2.5m

Volume of cuboid = Length × Breadth × Height

= 4.5 × 2 × 2.5

= 22.5 m^{3}

**Question 2.**Find the capacity of the tanks with the following internal dimensions. Express the capacity in cubic meters and liters for each tank.

**Answer:**i: Length = 3m 20cm = 3.2m

Breadth = 2m 90cm = 2.9m

Height = 1m 50cm = 1.5m

Volume of cuboid = Length × Breadth × Height

= 3.2 × 2.9 × 1.5

= 13.92 m^{3}

ii: Length = 2m 50cm = 2.5m

Breadth = 1m 60cm = 1.6m

Height = 1m 30cm = 1.3m

Volume of cuboid = Length × Breadth × Height

= 2.5 × 1.6 × 1.3

= 5.2 m^{3}

iii: Length = 7m 30cm = 7.3m

Breadth = 3m 60cm = 3.6m

Height = 1m 40cm = 1.4m

Volume of cuboid = Length × Breadth × Height

= 7.3 × 3.6 × 1.4

= 36.792 m^{3}

**Question 3.**What will happen to the volume of a cube if the length of its edge is reduced to half? Is the volume get reduced? If yes, how much?

**Answer:**Let x be the length of the cube

Volume of cube = (side)^{3}

= x^{3}

If the length of its edge is reduced to half, then length would be =

Now, Volume of cube =

=

Yes, the volume gets reduced by m^{3}.

**Question 4.**Find the volume of each of the cube whose sides are.

(i) 6.4 cm (ii) 1.3 m (iii) 1.6 m.

**Answer:**(i) Side = 6.4cm

Volume of cube = (side)^{3}

= (6.4) ^{3}

= 6.4 × 6.4 × 6.4

= 262.144 cm^{3}

(ii) Side = 1.3cm

Volume of cube = (side)^{3}

= (1.3) ^{3}

= 1.3 × 1.3 × 1.3

= 2.197 m^{3}

(iii) Side = 1.6m

Volume of cube = (side)^{3}

= (1.6) ^{3}

= 1.6 × 1.6 × 1.6

= 4.096 m^{3}

**Question 5.**How many bricks will be required to build a wall of 8 m long, 6m height and 22.5 cm thick, if each brick measures 25 cm by 11.25 cm by 6 cm?

**Answer:**Measurements of Wall:

Length = 800cm Breadth = 600cm and Height = 22.5cm

Volume of wall = Length × Breadth × Height

= 800 × 600 × 22.5

Measurements of Brick:

Length = 25cm Breadth = 11.25cm and Height = 6cm

Volume of wall = Length × Breadth × Height

= 25 × 11.25 × 6

Number of bricks required build a wall =

=

= 32 × 100 × 2

= 64 × 100

= 6400

Hence, 6400 bricks are required to build the wall.

**Question 6.**A cuboid is 25 cm long, 15 cm broad, and 8 cm high. How much of its volume will differ from that of a cube with the edge of 16 cm?

**Answer:**Measurement of cuboid

Length = 25 cm Breadth = 15 cm and Height = 8 cm

Volume of cuboid = Length × Breadth × Height

= 25 × 15 × 8

= 3000 cm^{3}

Measurement of cube

Side = 16cm

Volume of cube = (side)^{3}

= (16) ^{3}

= 16 × 16 × 16

= 4096 cm^{3}

Difference between the volumes = 4096 – 3000 cm^{3} = 1096 cm^{3}

Volume of cuboid differs from volume of cube by 1096 cm^{3}.

**Question 7.**A closed box is made up of wood which is 1cm thick. The outer dimensions of the box is 5 cm × 4 cm × 7 cm. Find the volume of the wood used.

**Answer:**Measurement of box from outside:

Length = 5 cm Breadth = 4 cm and Height = 7 cm

Volume of cuboid = Length × Breadth × Height

= 5 cm × 4 cm × 7 cm

= 140 cm^{3}

Measurement of box from the inside

Length = 4 cm

Breadth = 3 cm and

Height = 6 cm

Volume of cuboid = Length × Breadth × Height

= 4 cm × 3 cm × 6 cm

= 72 cm^{3}

Volume of wood used = volume of the box from outside – volume of the box from inside

= 140 – 72

= 68 cm^{3}

**Question 8.**How many cubes of edge 4cm, each can be cut out from cuboid whose length, breadth and height are 20 cm, 18 cm and 16 cm respectively.

**Answer:**Measurement of cuboid

Length = 20 cm Breadth = 18 cm and Height = 16 cm

Volume of cuboid = Length × Breadth × Height

= 20 × 18 × 16

= 5760 cm^{3}

Measurement of cube

Side = 4 cm

Volume of cube = (side)^{3}

= (4) ^{3}

= 4 × 4 × 4

= 64 cm^{3}

Number of cube which can be cut from the cuboid =

=

=

= 90

90 cubes can be cut out from the cuboid.

**Question 9.**How many cuboids of size 4 cm × 3 cm × 2 cm can be made from a cuboid of size 12 cm × 9 cm × 6 cm?

**Answer:**Measurement of bigger cuboid

Length = 12 cm Breadth = 9 cm and Height = 6 cm

Volume of cuboid = Length × Breadth × Height

= 12cm × 9cm × 6cm

Measurement of smaller cuboid

Length = 4 cm Breadth = 3 cm and Height = 2 cm

Volume of cuboid = Length × Breadth × Height

= 4cm × 3cm × 2cm

Number of smaller cuboids which can be made from bigger cuboid

=

=

= 3 × 3 × 3

= 27 cuboids

27 cuboids of smaller cuboids can be made from bigger cuboid.

**Question 10.**A vessel in the shape of a cuboid is 30 cm long and 25 cm wide. What should be its height to hold 4.5 liters of water?

**Answer:**We know that,

1 liter is 1000cm^{3},

∴ 4.5 liters = 4.5 × 1000 = 4500 cm^{3}

Measurement of vessel

Length = 30 cm,

Breadth = 25cm,

And Height =?

Let the height be h cm.

We are given the capacity which this vessel can hold i.e. the volume of the vessel.

Volume of vessel = Length × Breadth × Height

4500 = 300 × 25 × h cm

4500 = 750 × h

h =

h =

h = 6 cm

Hence, height of the vessel is 6cm which can hold 4.5 liters.

**Question 1.**

Find the volume of the cuboid whose dimensions are given below.

**Answer:**

i: Length = 8.2 m Breadth = 5.3m and Height = 2.6m

Volume of cuboid = Length × Breadth × Height

= 8.2 × 5.3 × 2.6

= 112.996 m^{3}

ii: Length = 5.0 m Breadth = 4.0m and Height = 3.5m

Volume of cuboid = Length × Breadth × Height

= 5 × 4 × 3.5

= 70 m^{3}

iii: Length = 4.5 m Breadth = 2m and Height = 2.5m

Volume of cuboid = Length × Breadth × Height

= 4.5 × 2 × 2.5

= 22.5 m^{3}

**Question 2.**

Find the capacity of the tanks with the following internal dimensions. Express the capacity in cubic meters and liters for each tank.

**Answer:**

i: Length = 3m 20cm = 3.2m

Breadth = 2m 90cm = 2.9m

Height = 1m 50cm = 1.5m

Volume of cuboid = Length × Breadth × Height

= 3.2 × 2.9 × 1.5

= 13.92 m^{3}

ii: Length = 2m 50cm = 2.5m

Breadth = 1m 60cm = 1.6m

Height = 1m 30cm = 1.3m

Volume of cuboid = Length × Breadth × Height

= 2.5 × 1.6 × 1.3

= 5.2 m^{3}

iii: Length = 7m 30cm = 7.3m

Breadth = 3m 60cm = 3.6m

Height = 1m 40cm = 1.4m

Volume of cuboid = Length × Breadth × Height

= 7.3 × 3.6 × 1.4

= 36.792 m^{3}

**Question 3.**

What will happen to the volume of a cube if the length of its edge is reduced to half? Is the volume get reduced? If yes, how much?

**Answer:**

Let x be the length of the cube

Volume of cube = (side)^{3}

= x^{3}

If the length of its edge is reduced to half, then length would be =

Now, Volume of cube =

=

Yes, the volume gets reduced by m^{3}.

**Question 4.**

Find the volume of each of the cube whose sides are.

(i) 6.4 cm (ii) 1.3 m (iii) 1.6 m.

**Answer:**

(i) Side = 6.4cm

Volume of cube = (side)^{3}

= (6.4) ^{3}

= 6.4 × 6.4 × 6.4

= 262.144 cm^{3}

(ii) Side = 1.3cm

Volume of cube = (side)^{3}

= (1.3) ^{3}

= 1.3 × 1.3 × 1.3

= 2.197 m^{3}

(iii) Side = 1.6m

Volume of cube = (side)^{3}

= (1.6) ^{3}

= 1.6 × 1.6 × 1.6

= 4.096 m^{3}

**Question 5.**

How many bricks will be required to build a wall of 8 m long, 6m height and 22.5 cm thick, if each brick measures 25 cm by 11.25 cm by 6 cm?

**Answer:**

Measurements of Wall:

Length = 800cm Breadth = 600cm and Height = 22.5cm

Volume of wall = Length × Breadth × Height

= 800 × 600 × 22.5

Measurements of Brick:

Length = 25cm Breadth = 11.25cm and Height = 6cm

Volume of wall = Length × Breadth × Height

= 25 × 11.25 × 6

Number of bricks required build a wall =

=

= 32 × 100 × 2

= 64 × 100

= 6400

Hence, 6400 bricks are required to build the wall.

**Question 6.**

A cuboid is 25 cm long, 15 cm broad, and 8 cm high. How much of its volume will differ from that of a cube with the edge of 16 cm?

**Answer:**

Measurement of cuboid

Length = 25 cm Breadth = 15 cm and Height = 8 cm

Volume of cuboid = Length × Breadth × Height

= 25 × 15 × 8

= 3000 cm^{3}

Measurement of cube

Side = 16cm

Volume of cube = (side)^{3}

= (16) ^{3}

= 16 × 16 × 16

= 4096 cm^{3}

Difference between the volumes = 4096 – 3000 cm^{3} = 1096 cm^{3}

Volume of cuboid differs from volume of cube by 1096 cm^{3}.

**Question 7.**

A closed box is made up of wood which is 1cm thick. The outer dimensions of the box is 5 cm × 4 cm × 7 cm. Find the volume of the wood used.

**Answer:**

Measurement of box from outside:

Length = 5 cm Breadth = 4 cm and Height = 7 cm

Volume of cuboid = Length × Breadth × Height

= 5 cm × 4 cm × 7 cm

= 140 cm^{3}

Measurement of box from the inside

Length = 4 cm

Breadth = 3 cm and

Height = 6 cm

Volume of cuboid = Length × Breadth × Height

= 4 cm × 3 cm × 6 cm

= 72 cm^{3}

Volume of wood used = volume of the box from outside – volume of the box from inside

= 140 – 72

= 68 cm^{3}

**Question 8.**

How many cubes of edge 4cm, each can be cut out from cuboid whose length, breadth and height are 20 cm, 18 cm and 16 cm respectively.

**Answer:**

Measurement of cuboid

Length = 20 cm Breadth = 18 cm and Height = 16 cm

Volume of cuboid = Length × Breadth × Height

= 20 × 18 × 16

= 5760 cm^{3}

Measurement of cube

Side = 4 cm

Volume of cube = (side)^{3}

= (4) ^{3}

= 4 × 4 × 4

= 64 cm^{3}

Number of cube which can be cut from the cuboid =

=

=

= 90

90 cubes can be cut out from the cuboid.

**Question 9.**

How many cuboids of size 4 cm × 3 cm × 2 cm can be made from a cuboid of size 12 cm × 9 cm × 6 cm?

**Answer:**

Measurement of bigger cuboid

Length = 12 cm Breadth = 9 cm and Height = 6 cm

Volume of cuboid = Length × Breadth × Height

= 12cm × 9cm × 6cm

Measurement of smaller cuboid

Length = 4 cm Breadth = 3 cm and Height = 2 cm

Volume of cuboid = Length × Breadth × Height

= 4cm × 3cm × 2cm

Number of smaller cuboids which can be made from bigger cuboid

=

=

= 3 × 3 × 3

= 27 cuboids

27 cuboids of smaller cuboids can be made from bigger cuboid.

**Question 10.**

A vessel in the shape of a cuboid is 30 cm long and 25 cm wide. What should be its height to hold 4.5 liters of water?

**Answer:**

We know that,

1 liter is 1000cm^{3},

∴ 4.5 liters = 4.5 × 1000 = 4500 cm^{3}

Measurement of vessel

Length = 30 cm,

Breadth = 25cm,

And Height =?

Let the height be h cm.

We are given the capacity which this vessel can hold i.e. the volume of the vessel.

Volume of vessel = Length × Breadth × Height

4500 = 300 × 25 × h cm

4500 = 750 × h

h =

h =

h = 6 cm

Hence, height of the vessel is 6cm which can hold 4.5 liters.