Question

External dimensions of a wooden box is 30 cm x 40 cm x 50 cm. If the thickness of the wood is 2 cm all around, then find the volume of the wood used for the box.

• A. 16,944 cm${}^3$
• B. 15,944 cm${}^3$
• C. 18,944 cm${}^3$
• D. 17,944 cm${}^3$

Answer 1

The correct option is A 16,944 cm${}^3$

Given, external dimensions length, breadth and height of the box are 30 cm, 40 cm and 50 cm respectively.

$\because$ Volume of cuboid = $\text{length}\times \text{breadth}\times \text{height}$

$\therefore$ External volume of the box $=30\times 40\times 50$
= 60,000 cm${}^3$

The internal dimension = External dimension - (2 x thickness)

Since, the thickness of box is 2 cm so,
internal dimensions of the box:
length = 30 - 4 = 26 cm
breadth = 40 - 4 = 36 cm
height = 50 - 4 = 46 cm
Therefore, Internal volume of the box
$=26\times 36\times 46$
= 43,056 cm${}^3$

Volume of wood used = External Volume - Internal Volume
= 60,000 - 43,056
= 16,944 cm${}^3$