Given:
The ratio of the cuboid length, breadth, and height is
27:8:1, respectively.
Total Surface area of cuboid
=p Total surface area of cube
=q Formula Used:
Volume of cuboid
= length
× breadth
× height
Volume of cube
=( side )3 Total surface area of cuboid
=2(lb+bh+hl) Total surface area of cube
=6( Side )2 Calculation:
Let the cuboid length, breadth, and height be
27k,8k,k respectively.
The total surface area of cuboid
=2(27k×8k+8k×k+k×27k) ⇒p=2k2(216+8+27) ⇒p=2k2(251) ⇒p=502k2 The cuboid is melted and recast into a cube of side 'a'.
⇒ Volume of cuboid
= Volume of a cube
⇒1×b×h=a×a×a ⇒27k×8k×k=a3 ⇒216k3=a3 ⇒a=6k Now the total surface area of a cube
q=6(6k)2 ⇒q=216k2 Therefore, the required ratio
= ⇒= ∴ The required value of
is