Question

Into a circular drum of radius \[4.9m\] and height \[3.6m,\] how many full bags of grain can be emptied if the space required for each given bag is \[1.8{m^3}?{\text{ }}(Take = {\text{ }}3.14)\]

Answer 1

Hint: To solve the problem, we will simply calculate the volume of the circular drum first and then divide the volume of the drum by the volume of \[1\]bag to find the total no. of bags.

Complete step-by-step answer:
We are given that radius of drum
\[\left( {Circular{\text{ }}Frum} \right){\text{ }} = {\text{ }}4.6m\]
Height of Drum \[ = {\text{ }}3.6m\]
We need to find how many full bags can be emptied if space required for one \[ = 1.8{m^3}\]
So, we will calculate volume
Volume of Circular Drum \[ = \pi {r^2}h\]
$
   = 3.14 \times {(4.9)^2} \times 3.6 \\
   = 1086.18{m^3} \\
$
Volume of each bag \[ = 1.8{m^3}\left( {Given} \right)\]
\[\Rightarrow No.{\text{ }}of{\text{ }}bags = \dfrac{{volume{\text{ }}of{\text{ }}drum}}{{volume{\text{ }}of{\text{ }}each{\text{ }}bag}}\]
\[\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; = \dfrac{{1086.18}}{{1.8}} = 603.43\]
So, no. of bags \[ = {\text{ }}603.43\]
So, No. of bags that can be emptied \[ = {\text{ }}603\] bags

Note: It should be clearly understood that the volume of drums and total volume of bags is the same. We know the volume of the cylinder \[ = \pi {r^2}h\]. Also, to determine the number of bags we took the whole value as the number of bags can not be in decimals.