Question

A cube of metal, each edge of which measures $5$ $cm$, weighs \[0.625\] kg. What is the length of each edge of a cube of the same metal which weighs \[40\] kg?

Answer 1

Hint: We find the edge of the cube which weights is \[40\] kg
It is given that each edge length $5$ $cm$ and weight is \[0.625\] kg cube and the weights of another cube is \[40\] kg
First we find the ratio of the volume of both cubes and then find the ratio of the edges of both cubes.

Complete step-by-step answer:
Let us consider $a$, $v$ and $w$ to be the edge, volume and weight of the first cube respectively. And $A$, $V$ and $W$ to be the edge, volume and weight of the second cube respectively.
The ratio of the weights of both cubes
${W/w}$ = \[40:0.625\]
Multiply 1000 on both sides, we get
${W/w}$ = \[40 \times 1000:625\]
${W/w}$ = $40000:625$
Dividing 625 on both sides, we get
${W/w}$ = \[64:1\]
Now the ratio of the volumes of both cubes
${V/v}$ = \[64:1\]
Taking cube root on both sides and we get the ratio of the edges of both cubes
${A/a}$ = \[4:1\]
Therefore, it means that the edge of the second cube is 4 times the edge of the first cube and the edge of the first cube is $5$ $cm$.
So that we multiply the edge of the first cube by 4 to get the edge of the second cube.
Hence, we get the edge of the second cube $A$ = \[5 \times 4 = 20\] cm
Therefore, the edge of the cube $A$ = \[20\] cm, which weighs \[40\] kg
Therefore, the edge of the first cube length is $5$ $cm$ and the edges of the second cube is $20$ $cm$

Note: The volume of a cube is \[{(edge)^3}\]. So when we got the ratio of the edges of both cubes we did cube roots of their volume’s ratio