Question

Three cubes whose edges are 3 cm, 4 cm and 5 cm respectively are melted to form a single cube. Find the

surface area of the new cube.
(1) 210 cm2
(1) 213 cm2
(3) 224 cm2
(4) 216 cm2
​

Answer 1

Answer:

(4) 216 cm2

Step-by-step explanation:

Edge of 1st cube = 3cm

Volume of 1st cube = edge^3

=3^3

=27cm^3

Edge of 2nd cube=4cm

Volume of 2nd cube =4^3

=64cm^3

Edge of 3rd cube =5cm

Volume of 3rd cube =5^3

=125cm^3

Total volume of the 3 cubes =Volume of new cube

Volume of new cube = 27 +64+125cm^3

=216cm^3

Edge^3=216

Edge=6cm

Surface area of the new cube = 6×edge^2

=6×6^2

=216cm^2

Answer 2

Formula used:  1. volume of any cube = a*a*a  or ( a^3).

                        2. surface area of a cube= 6*a*a      , where a =side of cube .

Concept:

Since the three cubes are melted to form a new single cube,

the volume of the new cube=(sum of volumes of the cubes).

Working:

Now,sum of volumes of cubes=(3*3*3)+(4*4*4)+(5*5*5)=216 cm3

so, volume of new single cube=216

=> a^3=216

=>a=cube root of(216)

=>a=6 cm      , where a= side of the single cube.

Surface area of the new cube= 6*(6^2)

                                                  =6*6*6

                                                   =216 cm2