AP State Syllabus AP Board 8th Class Maths Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 Textbook Questions and Answers.

## AP State Syllabus 8th Class Maths Solutions 14th Lesson Surface Areas and Volumes Exercise 14.2

Question 1.

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

Solution:

Question 2.

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

Solution:

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?

Solution:

Volume of a cube of side (s) is V_{1} = a^{3}

If the length of the side is reduced by half then

s = \(\frac{\mathrm{a}}{2}\)

∴ Volume of cube (V_{2} ) = s^{3}

∴ V_{2} = \(\frac { 1 }{ 8 }\) × V_{1}

∴ V_{1} = 8V_{2}

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.

Solution:

Volume of a cube(V) = a^{3}

i) a = 6.4 cm

ii) a = 1.3 m

iii) a = 1.6 m

V = (6.4)^{3
}Volume of a cube (V) = a^{3
}= 6.4 × 6.4 × 6.4

= 262.144 cm^{3
}

V = (1.3)^{3}

= 1.3 × 1.3 × 1.3

= 2.197 m^{3
}

V = (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 thici if each brick measures 25 cm by 11.25 cm by 6 cm?

Solution:

The volume of a wall of measures

8 m × 22.5 cm × 6 m

(V_{1}) = l_{1}b_{1}h_{1}

= 8 m × 22.5 cm × 6 m

= 800 cm × 22.5 cm × 600 cm

The volume of a brick each measures

25 cm × 11.25 cm × 6 cm

(V_{2}) = l_{2}b_{2}h_{2}

= 25 × 11.25 × 6 cm^{3}

∴ The no.of bricks will be required

= 32 × 2 × 100 = 6400

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’?

Solution:

Volume of a cuboid (V_{1}) of measures

= 25 cm, b = 15 cm, h = 8 cm.

V_{1} = 25 × 15 × 8 = 3000 cm^{3}

Volume of a cube of measure side (s) = 16 cm is

V_{2} = (s)^{3} = (16)^{3} = 16 × 16 × 16

= 4096 cm^{3}

The difference between their volumes

= V_{2} – V_{1}

= 4096 – 3000

= 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.

Solution:

The volume of a box formed with outer measures 5 cm × 4 cm × 7 cm

V_{1} = l × b × h

= 5 × 4 × 7

∴ V_{1} = 140 cm^{3}

Inner measures

= l – 2w, b – 2w, h – 2w

= (5 – 2 × 1), (4 – 2 × 1), (7 – 2 × 1)

= (5 – 2), (4 – 2), (7 – 2)

= 3 cm, 2 cm, 5 cm

∴ Volume of a box formed with inner measures

V_{2} = (l – 2w)(b – 2w)(h – 2w)

= 3 × 2 × 5 = 30 cm^{3}

∴ The volume of wood used = V_{1} – V_{2}

= 140 – 30 = 110 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

Solution:

The volume of a cuboid formed with the measures 20 cm × 18 cm × 16 cm

(V_{1}) = l_{1}b_{1}h_{1} = 20 × 18 × 16

Volume of a cube (V_{2}) = s^{3}

s = 4 cm (given)

∴ V_{2} = (s)^{3} = (4)^{3}= 4 × 4 × 4 cm^{3}

∴ No.of cubes are required

= \(\frac{V_{1}}{V_{2}}=\frac{20 \times 18 \times 16}{4 \times 4 \times 4}\)

= 90

Question 9.

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

Solution:

Volume of a cuboid of measures 12 cm × 9 cm × 6 cm

V_{1} = l × b × h = 12 × 9 × 6

Volume of the smaller cuboid of measures 4 cm × 3 cm × 2 cm

V_{2} = l_{2}b_{2}h_{2} = 4 × 3 × 2

∴ No.of cuboids are made

= \(\frac{V_{1}}{V_{i}}=\frac{12 \times 9 \times 6}{4 \times 3 \times 2}\) = 27

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 litres of water ?

Solution:

Length of a cuboidal vessel (l) = 30 cm

breadth (b) = 25 cm

height (h) = ?

The volume of water m a cuboidal vessel = 4.5 Lts.

= 4.5 × 1000 cm^{3}

= 4500 cm^{3}

∴ l × b ×h = 4500

⇒ 30 × 25 × h = 4500

⇒ h = \(\frac{4500}{30 \times 25}\)

∴ h = 6 cm

∴ Height of the vessel (h) = 6 cm