Question

a cuboid of dimensions 45 cm into 25 cm into 24 cm is melted to form 27 identical cubes find the dimension of each cube.​

Answer 1

Answer:

The dimension of each cube is $10\ cm$.

Step-by-step explanation:

When a cuboid melts to form cubes the volume of the cuboid and the total volume of the cubes will be the same. So we can compare the volume of each to find the number of cubes made out of the cuboid.

The volume of cuboid is,

$Volume= length\times breadth\times height$

The dimensions of the cuboid are $45\ cm, 25\ cm$ and $24\ cm$. Thus we have the volume as,

$Volume = 24 \times 45\times 25=27000\ cm^3$

Let $a$ be the dimension of each cube. Then the volume is,

$Volume =a^3$

Since there are 27 cubes, the total volume is,

$Total\ Volume = 27a^3$

So equating the volumes, we get

$\implies 27a^3=27000\\\\\implies a^3=\dfrac{27000}{27}=1000 \\\\a=\sqrt[3]{1000}=10\ cm$

The dimension of each cube is $10\ cm$.