Question

A cupboard made up of wood has the inner measures as 120 cm, 70 cm and 45 cm. If the thickness of the wood is 2.5 cm, then find the volume of the wood.
A. $90750c{m^3}$
B. $82125c{m^3}$
C. $47000c{m^3}$
D. \[85000c{m^3}\]

Answer 1

Hint: We will first calculate the external volume of the cupboard using the formula, is $lbh$, where $l$ is the length, $b$ is the breadth and $h$ is the height of the cuboid. Next, find the external dimensions of the cupboard by adding thickness and then find its volume. At last, subtract internal volume from external volume of the cupboard to find the volume of the wood.

Complete step-by-step answer:
We are given that the measurement of the cupboard is 120 cm, 70 cm and 45 cm and the thickness of the wood is 2.5 cm.
We know that the volume of the cuboid is $lbh$, where $l$ is the length, $b$ is the breadth and $h$ is the height of the cuboid.

We will first calculate the internal volume of the cupboard.
Volume=lbh
$\Rightarrow$ $120 \times 70 \times 45 = 378000c{m^3}$
Now, we will calculate the external measurements of the cupboard by adding the thickness of the wood on both the sides.
The length of the cupboard is $120 + 2.5 + 2.5 = 125cm$, the breadth of the cupboard is $70 + 2.5 + 2.5 = 75cm$ and the height of the cupboard is $45 + 2.5 + 2.5 = 50cm$
Now, the external volume of the cupboard is $125 \times 75 \times 50 = 468750c{m^3}$
We can now calculate the volume of the wood by subtracting internal volume from external volume of the cupboard.
$\Rightarrow$ $468750 - 378000 = 90,750c{m^3}$
Hence, the volume of the wood is $90,750c{m^3}$
Thus, option A is correct.

Note: Volume is the space enclosed any object. When we calculate the external dimensions we will add the thickness of the wood on both the sides of the internal dimensions. Volume is always measured in cubic units.