Question

Three metal cubes whose edges are 9cm, 12cm and 15 cm are melted together and formed into one cube.
a) Find the edge of the new cube formed b) Find the surface area of the new cube formed​

Answer 1

Step-by-step explanation:

We know that volume does not change.

Volume of cube =x

3

where x is side of cube

⇒15

3

+12

3

+9

3

=a

3

a

3

=5832

a=18cm

⇒ Diagonal of cube =

3

a

=18

3

Hence, the answer is 18

3

.

Answer 2

Answer:

a) 18cm

b) 1944 ${cm}^{2}$

Step-by-step explanation:

We are given that

• Three metal cubes with edges 9cm, 12cm and 15 cm
• They are melted together and formed into one cube

We know that

• When solids are melted their volume remains the same

Therefore,

Let the side/edge be a cm

$\implies$ Volume of new cube = ${a}^{3}$

${15}^{3}$ + ${12}^{3}$ + ${9}^{3}$ = ${a}^{3}$

${a}^{3}$ = 5832

$\therefore$ a = 18cm

Now,

Surface area of cube, A = 6 ${a}^{2}$

$\implies$ A = 6 × 18 × 18

$\therefore$ A = 1944 ${cm}^{2}$