Question

Three metal cubes with edges 15 cm., 12 cm. and 9 cm. respectively are melted together and formed into a simple cube. Find the diagonal of this cube.

Answer 1

volume of cube _ side^3
therefore the the volumes of three cubes are
3375cucm,1728 cucm, 729 cucm .
volume of three cube= volume of simple cube
$3375 + 1728 + 729 = x {}^{3} \\ 5832 = {x}^{3} \\ x = 18$
the edge of new cube is 18cm.
a face of cube is square.
diagonal of square = side× √2
18√2
therefore diagonal of the new cube is 18√2
hope this helps you.
don't forget to do it brainleist.

Answer 2

volume of cube _ side^3

therefore the the volumes of three cubes are

3375cucm,1728 cucm, 729 cucm .

volume of three cube= volume of simple cube

3375 + 1728 + 729 = x^3

5832 = x^3

x = 18

the edge of new cube is 18cm.

a face of cube is square.

diagonal of square = side× √2

18√2

therefore diagonal of the new cube is 18√2

Hope this helps!