Question

Two cylindrical containers are similar. The larger one has internal cross- section area of 45cm^2 and can hold 0.945 litres of liquid when full. The smaller container has internal cross- section area of 20cm^2.
(a) Calculate the capacity of the smaller container.
(b) The larger container is filled with juice to a height of 13 cm. Juice is then drawn from it and emptied into the smaller container until the depths of the juice in both containers are equal. Calculate the depths of juice in each container.

Answer 1

If the scale factor is r, then
the area grows by r^2
the volume grows by r^3
So, if the area scales by 20/45, the volume scales by (20/45)^(3/2).
The smaller cylinder has cross-section area of .945*(20/45)^(3/2) = 0.28 cm^3

If x cm is transferred to the smaller container, then

13-x = (45/20)x
x = 4

check:
13-4 = 9
45*4 = 180 transferred out
20*9 = 180 transferred in
The depth in both containers is 9 cm

Answer 2

yes

Answer 3

What about section c of the question