Question

A closed box is made of wood which is 1.8 cm thick. Its external
dimensions are 84 cm x 64 cm x 50 cm. Find:
(i) the capacity of the box.
(ii) the volume of the wood used in making the box.
(iii) the weight of the empty box if icm' of wood weighs 6.8 g.
​

Answer 1

Given :-

• A closed box of wood is 1.8cm thick

• External dimensions are 84 cm * 64cm * 50cm

Solution 1 :-

[ Here, We have to find capacity so we have to find it internal dimensions ]

• Internal length = 84 - 1.8 = 82.2

• Internal breath = 64 - 1.8 = 62.2

• Internal Height = 50 - 1.8 = 48.2

Now,

The capacity ( volume) of the box

Using formula ,

Volume of rectangle = Length * Breath * height

Volume of wooden box

= 82.2 * 62.2 * 48.2

= 246438.88

Solution 2 :-

Here, we have to find the volume of wood

• The External volume of wood

= 84 * 64 * 50

= 268800

• The internal volume of wood

= 246438.88

Now,

The volume of wood

= External volume - internal volume

= 268800 - 246438.88

= 22361.12

Hence, The volume of wood = 22361.12 cm^3

Solution 3 :-

• The volume of 1 cm of wood = 6.8g $.$

Here,

• The total volume of wood = 22361.12cm^3

Now,

• The weight of the wood

= 22361.12 * 6.8

= 152,055.616

Answer 2

QuestioN :

A closed box is made of wood which is 1.8 cm thick. Its external  dimensions are 84 cm x 64 cm x 50 cm. Find:

(i) the capacity of the box.

(ii) the volume of the wood used in making the box.

(iii) the weight of the empty box if icm' of wood weighs 6.8 g.

GiveN :

• Wood which is 1.8 cm thick.

• External dimensions are 84 cm x 64 cm x 50 cm.

To FiNd :

• Capacity of internal dimensions.

FormulA :

• Volume of rectangle = Length × Breath × height
• External Volume - Internal Volume

ANswer :

152,055.616

SolutioN :

1).

• Internal length = 84 - 1.8 = 82.2  

• Internal breath = 64 - 1.8 = 62.2  

• Internal Height = 50 - 1.8 = 48.2

The Volume of a wooden box

= 82.2 × 62.2 × 48.2

= 246438.88

Hence, The capacity of the box = 246438.880.

2).

The External volume of wood

= 84 × 64 × 50

= 268800  

The internal volume of wood

= 246438.88

Now,

The volume of wood

• External volume - internal volume

= 268800 - 246438.88

= 22361.12

Hence, The volume of wood = 22361.12 $cm^3$

3).

The volume of 1 cm of wood = 6.8g

Here,  

The total volume of wood = 22361.12$cm^3$

Now,

The weight of the wood

= 22361.12 × 6.8

= 152,055.616

Hence, The weight of the empty box = 152,055.616