Question

three metallic cube of side 3cm,4cm5,cm respectively are melted and ate recaste into a single cube. find the total surface area of the new cube

Answer 1

The volume of the three cubes
v = (3 x 3 x 3) + (4 x 4 x 4) + (5 x 5 x 5)
= 27 + 64 + 125
= 216

Side of new cube formed by melting above 3 cubes = cube root of 216 = 6 cm
The surface area of new cube = 6 x (6 x 6) = 216 sq sm

Answer 2

Hi ,

Let a = 3cm , b = 4cm , c = 5cm

are the sides of three metallic cubes ,

melted and cast into a new cube

whose side is ' d ' cm

Volume of the new cube = volumes

of the three cubes

d³ = a³ + b³ + c³

= 3³ + 4³ + 5³

= 27 + 64 + 125

= 216

d³ = 6³

d = 6 cm

Therefore ,

Total surface area of the new cube

= 6d²

= 6 × 6²

= 216 cm²

I hope this helps you.

: )