Question

The outer length, breadth and height of a box open at the top are $10$ dm, $8$ dm and $5$ dm respectively. If the thickness of the wood is $1$ dm, then the total surface area of the box is

• A. $424$ dm${}^2$
• B. $452$ dm${}^2$
• C. $451$ dm${}^2$
• D. $483$ dm${}^2$

Answer 1

The correct option is A $424$ dm${}^2$

Outer Surface Area $=lb+2bh+2lh$
$=8\times 10+2(5\times 10)+2(5\times 8)$
$=80+100+80=260$ dm${}^2$
Inner Surface Area $=(l-2)(b-2)+2(b-2)(h-2)+2(l-2)(h-2)$
$=6\times 8+2(3\times 8)+2(3\times 6)$
$=48+48+36=132$ dm${}^2$
Area of the upper surface $=lb-(l-2)(b-2)$
$=80-48=32$ dm${}^2$
Total Surface Area$=260+132+32$
$=424$ dm${}^2$