# 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:

- 280 cm
^{2} - 272 cm
^{2} - 286 cm
^{2} - 290 cm
^{2}

**Answer: 286 cm ^{2}**

**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 a ^{2}**

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.