Question

What is the total cost of oil in a cubical container of side 2m if it is measured and sold using a cubical vessel of height 10 cm and the cost is Rs. 50 per measure.

Answer 1

Hint: First of all, assume there are ‘n’ small cubical vessels of 10 cm. Now equate the volume of the big cubical container of 2m to the volume of a cubical vessel. Get the value of n, multiply it to 50 to get the total cost of oil.

Complete step-by-step answer:

Here, we have to find the cost of the oil in a cubical container of side 2m if it is measured and sold using a cubical vessel of height 10 cm and the cost is Rs. 50 per measure. Basically in the question, we have a big cubical container of side 2m. Now, the oil from this big cubical container is poured in small cubical vessels of side 10 cm each costing Rs. 50.


So, to find the total cost of oil in a cubical container, we first have to find the total number of small cubical vessels needed.

Let us assume, there are total n cubical vessels of side 10 cm. We know that the oil from a big container is poured in a small cubical vessel, then the volume of the big container is equal to the volume of n cubical vessels. So, we get,

(Volume of the cubical container of side 2m) = n (Volume of the cubical vessel of side 10 cm)

\[\Rightarrow {{V}_{C}}=n{{V}_{S}}....\left( i \right)\]

We know that the volume of the cube \[={{\left( \text{side} \right)}^{3}}\]

So, we get the volume of the cubical container of side 2m \[\left( {{V}_{C}} \right)\] = \[{{\left( 2m \right)}^{3}}=8{{m}^{3}}\]

\[\Rightarrow 8\times {{\left( 100 \right)}^{3}}c{{m}^{3}}\]

\[{{V}_{C}}=8\times {{10}^{6}}c{{m}^{3}}\]

Also, we get the volume of the cubical vessel of side 10 cm, \[\left( {{V}_{S}} \right)={{\left( 10cm \right)}^{3}}\]

\[{{V}_{S}}={{10}^{3}}c{{m}^{3}}\]

So, by substituting the value of \[{{V}_{C}}=8\times {{10}^{6}}c{{m}^{3}}\] and \[{{V}_{S}}={{10}^{3}}c{{m}^{3}}\] in equation (i), we get,

\[8\times {{10}^{6}}=n\left( {{10}^{3}} \right)\]

By dividing both the sides by \[{{10}^{3}}\], we get,

\[\dfrac{8\times {{10}^{6}}}{{{10}^{3}}}=n\]

\[n=8\times {{10}^{3}}=8000\text{ vessels}\]

Now, the cost of 1 vessel = Rs. 50. So, we get the cost of 8000 vessels \[=8000\times Rs.50\]

\[=Rs.40\times {{10}^{4}}\]

\[Rs.4\times {{10}^{5}}\]

Hence, we get the total cost of oil in cubical containers as Rs. 400000.

Note: In these types of questions, students should take great care of the units and always take all the quantities in the same units to avoid any mistakes. Also, some students answer the value of n = 3000, but they must not forget to multiply it to 50 to get the final cost of oil in cubical containers of side 10 cm.