Question

The weight of a cubic meter of a certain metal is 480 kg. It is melted and then rolled into a square bar 4m long. Now, an exact cube is cut from it. Find the weight of the cube.
(a) 240 kg
(b) 80 kg
(c) 120 kg
(d) 60 kg

Answer 1

Hint: First, here we have to find the volume of a square bar having weight the same as 480kg using the formula $volume=length\times breadth\times height$ . Then, this square is cut into an exact cube. So, here we will assume all the dimensions equal to 1 unit and again we will find the volume of the cube. Then using the unitary method, we will find the weight of the cube.

Complete step by step answer:
Here, we are given a total weight of metal in the form of cubic meters i.e, 480kg. This means that the formula of volume is going to be used as its unit is in cubic form.
Now, it is melted and then rolled into a square bar having a length of 4m. This, we can consider in the form of square bar having width and height of 1 meter.

Here, we will find volume of this square bar using the formula $volume=length\times breadth\times height$
On substituting the values, we get as
$volume=4\times 1\times 1=4{{m}^{3}}$ ………………………………..(1)
Now, this square base is cut in such a way that it forms the cube. So, diagram can be imagined as

Again, we will find the volume of this cube taking length, breadth and height as 1 meter. So, on using the formula, we get
$volume=1\times 1\times 1=1{{m}^{3}}$ …………………………..(2)
Now, when metal is rolled into a square bar its weight remains the same i.e. 480 kg. We have to find when it is cut to make a cube what is its weight. So, here we will be using unitary method and on solving we get
$\begin{aligned} & 4{{m}^{3}}=480kg \\\ & 1{{m}^{3}}=? \\\ \end{aligned}$
On further solving, we get
$=\dfrac{480}{4}=120kg$
Thus, the weight of the cube is 120kg.
Hence, option (c) is correct.

Note: Be careful in the cube part. It is told that an exact cube is to be cut. Students might consider that the square bar is exactly cut from the middle which will be in cube form, so length will be 2m and breadth height will be the same as 1meter. So, the volume of the cube will be $2{{m}^{3}}$ . And on using unitary method, we get equation as
$\begin{aligned} & 4{{m}^{3}}=480kg \\\ & 2{{m}^{3}}=? \\\ \end{aligned}$
$=\dfrac{480\times 2}{4}=240kg$
So, the answer will be 240kg which is incorrect. But we should know that cubes have equal sides of measure so, length is to be considered as 1m only. Do not make this silly mistake.