Question

The dimensions of an open box are $50$ cm, $40$ cm and $23$ cm. Its thickness is $3$ cm. If $1$ cubic cm of metal used in the box weighs $0.5$ gms, find the weight of the box.

• A. $6.2$ kg
• B. $12$ kg
• C. $7.99$ kg
• D. $8.04$ kg

Answer 1

Answer: (D)

$8.04$ kg

(See figure for clarity of information provided in question)

Volume of box $=$ volume of outer box $-$ volume of empty space

Volume outer box$=l\times b\times h=50\times 40\times 23{\text{cm}}^3$

Volume inner empty space $=l\times b\times h=44\times 34\times 20{\text{cm}}^3$

Volume of box $=23\times 50\times 40-44\times 20\times 34=16080{\text{cm}}^3$

Weight of box $=16080\times 0.5=8040$ gm $=8.04$ kg

NOTE:

1. Length of empty space $=$ length of box $-2\times$ thickness
2. Breadth of empty space $=$ breadth of box $-2\times$ thickness
3. Height of empty space $=$ length of box $-$ thickness