Question

The dimensions of a cuboid ice-cube are $50cm\times 30cm\times 20cm$. Find its weight in kg, if the weight of $1000c{{m}^{3}}$ is 900 gm.
A. 270 kg
B. 27 kg
C. 2.7 kg
D. 0.27 kg

Answer 1

Hint: In order to solve this question, we will first calculate the volume of the ice cube by drawing the figure to get a better understanding and by using the formula $V=l\times b\times h$, we will use the given relation to get the weight in gm from $c{{m}^{3}}$. We will then convert it into kg using the relation of 1 kg = 1000 gm to get our answer.

Complete step-by-step answer:
In this question, we have been asked to find the weight of a cuboidal ice-cube of dimensions $50cm\times 30cm\times 20cm$ into kg, when it is given that $1000c{{m}^{3}}$ is 900 gm. Now, to solve this question, we will first draw the figure as per the given conditions. So, the figure is given below.
 

Now, we know that the volume of a cuboid is given by $l\times b\times h$, where l = length, b = breadth and h = height respectively. In the above figure, we have represented 50 cm as the length of the ice-cube, 30 cm as the breadth and 20 cm as the height as per the dimensions given in the question. So, we get the volume of the ice-cube as,
$\begin{align}
  & V=50\times 30\times 20 \\
 & \Rightarrow V=30,000c{{m}^{3}} \\
\end{align}$
Now, we have been given that $1000c{{m}^{3}}$ weighs 900 gm. So, by unitary method, we can say that $1c{{m}^{3}}$ weighs $\dfrac{900}{1000}gm$. And therefore, we can say that, $30,000c{{m}^{3}}$ will weigh $\dfrac{900}{1000}\times 30,000gm$, which is 27,000 gm.
Now, we have been asked to find the weight of $50cm\times 30cm\times 20cm$ in kg. So, we will convert 27,000 gm into kg to get our answer. We know that 1 kg = 1000 gm. So, we can say that $1gm=\dfrac{1}{1000}kg$. And further we can say that $27000gm=\dfrac{27000}{1000}kg$, which is 27 kg.
Hence, we can say that the weight of $50cm\times 30cm\times 20cm$ is equal to 27 kg. Therefore, option B is the correct answer.

Note: While solving this question, there is a possibility of making calculation mistakes while finding the volume or weight or doing the conversion of gm into kg. And also, we should be careful while selecting the options, as they may appear similar and the difference might be that of a 0 or a decimal.