Question

A plate of metal 1 cm thick. 9 cm broad. 81 cm long is melted in to a cube. Find the
difference in the surface area of two solids.​

Answer 1

Answer:

Find surface area of plate

= 2(ab+ bc +ca )

=2(1×9 + 9×81 + 1 × 81 )

= 1638 cm2

Now volume = 1 × 9 × 81 = 729 cm3

Volume of new cube will be same . Assume a side of cube is a .

So

${a}^{3} = 729 \\ a = \sqrt[3]{729} = \sqrt[3]{ 9 \times 9 \times 9 } = 9 \: cm$

So surface area of cube

= 6 (a × a) = 6 × 9× 9 = 486 cm2

So difference

= 1638 - 486 = 1152 cm2

Answer 2

Answer:1152 cm^2

Step-by-step explanation:

Volume of plate = volume of cube

81*9*1=a^3

So a=9

Surface area of plate =2lb+lh+hb

=1638

Surface area of cube =6a^2

=6*9*9=486

Difference=1638-486=1152cm^2