Question

The internal dimensions of a closed box, made up of iron 1 cm thick, is 24 cm by 18 cm by 12 cm. Find the volume of iron in the box.

Answer 1

Hint: As it is given in the question, the box is made up of iron which is 1 cm thick, therefore, the box has two volumes, the inner volume and the outer volume. We will first calculate the inner volume using the dimensions given in the question. Then, we will have to calculate the outer dimensions of the box and then find the external volume of the box. Then, at last, we will subtract the internal volume from the external volume to find the volume of the iron in the box.

Complete step-by-step answer:
In this question, the box is made up of iron which is 1 cm thick, hence, the box is divided into 2 regions.
There will be an internal volume and an external volume.
We are given the internal dimensions of the box. So, we will calculate the internal volume of the box using the given dimensions.
\[{\text{Volume of the cuboid = length}} \times {\text{breadth}} \times {\text{height}}{\text{.}}\]
Hence, internal volume of the box is \[24 \times 18 \times 12 = {\text{ }}5184{\text{ c}}{{\text{m}}^{\text{3}}}\]
Next, we will find the outer dimensions of the box using the thickness of iron.
Since iron is 1 cm thick, therefore, each dimension will be increased by 1 cm from both sides.
That is, external length will be 24+1+1 = 26 cm
Similarly, external breadth will be 18+1+1=20 cm
And external height will be 12+1+1=14 cm.
Now, calculate the external volume of the box.
External volume of the box will be \[26 \times 20 \times 14 = {\text{ }}7280{\text{ c}}{{\text{m}}^3}\]
But, we want to calculate the volume of iron. To calculate the volume of iron, subtract the volume of the internal box from the volume of the external box.
7280-5184= 2096 cm3.\[7280 - 5184 = {\text{ }}2096{\text{ c}}{{\text{m}}^{\text{3}}}\]
Hence, the volume of the iron is 2096 \[{\text{c}}{{\text{m}}^{\text{3}}}\].

Note:- The box will be a cuboid, hence, the volume will be \[{\text{length}} \times {\text{breadth}} \times {\text{height}}\]. While calculating the external dimensions of the box, we have the additional 1 cm twice and not just once because the thickness of iron will increase the dimension on both sides. Also, mention the unit of the volume that is 3 cm for the final answer.