Question

The sum of length, breadth and height of a cuboid is $12$ cm long and its diagonal is $8$ cm. The total surface area of the cuboid is:

• A. $88$ sq cm
• B. $85$ sq cm
• C. $90$ sq cm
• D. $80$ sq cm

Answer 1

The correct option is D $80$ sq cm

$l+b+h=12cm$ ...(1)

$d=8cm$

$\Rightarrow \sqrt{l^2+b^2+h^2}=8$

$\Rightarrow l^2+b^2+h^2=64$ ...(2)

Now, ${(l+b+h)}^2=l^2+b^2+h^2+2lb+2bh+2hl$

$\Rightarrow {\left(12\right)}^2=64+2(lb+bh+hl)$

$\Rightarrow 2(lb+bh+hl)=144-64=80$

$\therefore$TSA of cuboid$=80c{m}^2$