Exercise 14.2
1. Find the volume of the cuboid whose dimensions are given below.
| Length (m) | Breadth (m) | Height (m) | |
|---|---|---|---|
| i | 8.2 | 5.3 | 2.6 |
| ii | 5.0 | 4.0 | 3.5 |
| iii | 4.5 | 2.0 | 2.5 |
Solution:
The volume of a cuboid is calculated using the formula: Volume = Length ×
Here's the solution presented in a table:
| Length (m) | Breadth (m) | Height (m) | Volume ( | |
|---|---|---|---|---|
| i | 8.2 | 5.3 | 2.6 | 8.2 × 5.3 × 2.6 = |
| ii | 5.0 | 4.0 | 3.5 | 5.0 × 4.0 × 3.5 = |
| iii | 4.5 | 2.0 | 2.5 | 4.5 × 2.0 × 2.5 = |
2. Find the capacity of the tanks with the following internal dimensions. Express the capacity in cubic meters and liters for each tank.
| Tank | Length | Breadth | Depth |
|---|---|---|---|
| (i) | 3 m | 20 cm | 2 m 90 cm |
| (ii) | 2 m 50 cm | 1 m 60 cm | 1 m 30 cm |
| (iii) | 7 m 30 cm | 3 m 60 cm | 1 m 40 cm |
Solution:
The capacity of a tank (or the volume of a cuboid) is calculated using the formula: Volume = Length × Breadth × Depth.
We will convert all dimensions to meters. Remember that 1
| Length (m) | Breadth (m) | Depth (m) | Volume (m³) | Capacity (liters) |
|---|---|---|---|---|
| 3.0 | 0.2 | 2.9 | ||
| 2.5 | 1.6 | 1.3 | | |
| 7.3 | 3.6 | 1.4 |
3. What will happen to the volume of a cube if the length of its edge is reduced to half? Is the volume reduced? If yes, how much?
Solution:
Let the original edge length of the cube be 's'.
The original volume of the cube is V1 =
If the edge length is reduced to half, the new edge length will be
The new volume of the cube is V2 =
Comparing the new volume (V2) with the original volume (V1):
V2 = (
The new volume is
It is reduced to
4. Find the volume of each of the cube whose sides are.
(i) 6.4 cm
Solution:
Volume of a cube =
(ii) 1.3 m
Solution:
Volume of a cube =
=
=
(iii) 1.6 m
Solution:
Volume of a cube =
=
=
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?
Solution:
Volume of the wall = long × height ×
Volume of the wall =
=
=
Volume of each brick =
=
Number of bricks =
=
=
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 the cuboid =
=
Volume of the cube =
=
Difference in volume =
=
7. A closed box is made up of wood which is 1cm thick. The outer dimensions of the box are 5 cm × 4 cm × 7 cm. Find the volume of the wood used.
Solution:
Outer volume =
=
The wood forms a shell around an empty space inside the box. The 1 cm thickness applies to both sides of each dimension
Inner dimensions: l =
b =
h =
Inner volume =
=
Volume of wood = Outer volume - Inner volume
=
=
8. How many cubes of edge 4cm, each can be cut out from a cuboid whose length, breadth and height are 20 cm, 18 cm and 16 cm respectively?
Solution:
Volume of the cuboid = 20 cm × 18 cm × 16 cm =
Volume of each cube =
=
Number of cubes =
=
=
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?
Solution:
Volume of the larger cuboid = 12 cm × 9 cm × 6 cm =
Volume of the smaller cuboid = 4 cm × 3 cm × 2 cm
=
Number of smaller cuboids =
=
=
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:
4.5 liters =
Volume of cuboid = length × breadth × height
4500
Height =
=