# What will be the Difference between the Surface Area of Two Solids? If

A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The difference between the surface area of the two solids is:

1. 280 cm2
2. 272 cm2
3. 286 cm2
4. 290 cm2

Explanation:-
The length, width and thick of a metal sheet = 27 cm, 8 cm, 1 cm.
Formula-
The surface area of a the metal sheet = 2 ( l x b + b x h + h x l )
Where, l = length, b = width  &  h = height.

Then, the surface area of  of the metal sheet = = 2 (27 x 8 + 8 x 1 + 1 x 27)
= 2 (216 + 8 + 27)
= 2 x 251
= 502 cm square

The volume of the metal sheet = the volume of the cube       (Given in the question)
Formula-
The volume of the metal sheet = l x b  x  h
Where, l = length , b = breadth  &  h = height

Then, the volume of the metal sheet = 27 x 8 x 1
= 216 cm cube  = Volume of the cube
Therefore, the side of a cube  = cube root of 216
= 6 cm
Formula-
The surface area of a cube =6 a2

Then, the surface area of cube = 6 (6)^2
= 6 x 36
= 216 cm square
The difference between the surface area of the two solids = 502 – 216
= 286 cm square
Hence, the answer is  (3) 286 cm square.

Anurag Mishra Professor Answered on 4th August 2015.