Question

A 20-cm metal cube was melted into 2 identical cuboids. The height of each cuboid was twice the original metal cube. The 2 identical cuboids had square bases. Find the length of one side of the square base of one cuboid. please help

Answer 1

Answer:

$20cm$

Step-by-step explanation:

Given: Side of metal cube =

$20cm$

Therefore, Volume of metal cube =

${(20cm)}^{3} \\ = 8000 {cm}^{3}$

Therefore, volume of each cuboid =

$8000 {cm}^{3} \div 2 \\ = 4000 {cm}^{3}$

Given, height of each cuboid =

$(height \: of \: cube) \div 2 \\ = 10cm$

Also, length and breadth of the cuboid are equal.

Therefore, we can take the side as s.

Therefore, we can say,

$10cm \: \times s \times s = 4000 {cm}^{3} \\ = > {s}^{2} = 4000 {cm}^{3} \div 10cm \\ = > {s}^{2} = 400 {cm}^{2} \\ = > s = \sqrt{400 {cm}^{2} } \\ = > s = 20cm \: (ans)$

Hope this helps.