Bunuel
It costs $2,250 to fill right circular cylindrical Tank R with a certain industrial chemical. If the cost to fill any tank with this chemical is directly proportional to the volume of the chemical needed to fill the tank, how much does it cost to fill right circular cylindrical Tank S with the chemical?
(1) The diameter of the interior of Tank R is twice the diameter of the interior of Tank S.
(2) The interiors of Tanks R and S have the same height.
DS14602.01
Quantitative Review 2020 NEW QUESTION
kaylaquijasWe are given that price is directly proportional to volume.
Price = k*Volume
2250 = k * Vr
(Vr is the volume of tank R)
We need the cost to fill tank S. If we can find the relation between the volume of tank R and volume of tank S, we can find the price of filling tank S. Say their volumes are same. Then tank S will also need $2250 to fill up. Say volume of tank S is twice the volume of tank R, then tank S will need $4500 to fill up and so on...
Volume of a tank R = pi*r^2*h (it depends on radius and height)
(1) The diameter of the interior of Tank R is twice the diameter of the interior of Tank S.
So tank S has half the diameter of tank R i.e. it has half the radius of tank R.
This means that the volume of tank S is one fourth the volume of tank R if their heights are the same. Else volume will depend on height too.
Not sufficient alone since we don't know the relation of their heights.
(2) The interiors of Tanks R and S have the same height.
Now we know that their heights are the same. But alone this is not sufficient because we don't have the relation of their radii.
Using both, we know that radius of S is 1/2 of the radius of tank R and height of tank S is the same as the height of tank R.
Volume of tank S = pi*r^2*h/4
Since the volume of tank S is only 1/4th of volume of tank R, price of filling it up will also be 1/4th of $2250 = $562.5
Though we don't need to do all these calculations.