Question

The maximum possible number of identical rectangular blocks are placed inside a rectangular carton. The rectangular blocks each have a length of $7$, a width of $5$, a height of $4$ and the rectangular carton has inside dimensions that are a length of $16$, a width of $15$ and a height of $14$. Calculate the total surface area of the rectangular blocks that are inside the rectangular carton.

• A. $1,348$
• B. $1,992$
• C. $2,656$
• D. $3,360$
• E. $3,984$

Answer 1

The correct option is E $3,984$

Given length $=7$, width $=5$ and height $=4$ of rectangular boxes

Then volume of rectangular box $=$ $7\times 5\times 4=140$

Then covered surface area of rectangular boxes $=$ $2(7\times 5+5\times 4+4\times 7)=2(35+20+28)=166$

And given length $=16$, width $=15$ and height $=14$ of rectangular carton

Then volume of rectangular carton $=$ $16\times 15\times 14=3360$

Then number of rectangularboxes placed in rectangular carton $=$ $\frac{3360}{140}=24$

So, total covered surface area of $24$ rectangular boxes $=$ $24\times 166=3984$