An oil tanker, cylindrical in shape, has a diameter 7 m and height 12 m. It supplies oil from two
outlets at rates which are in the ratio 2:3.
The first outlet (the one with a lesser rate) is supplying oil
in a cuboidal vessel with the base area 14
m2. And the second outlet is supplying oil in a triangular prism-shaped vessel with the base having
the side lengths 6 m, 8 m, and 10 m.
Find the height (or level) of the oil in each of the vessel after transferring the entire oil to these two
vessels through the outlets.
Answers
Answer:
Step 1: To find volume of cylindrical tank
Given: Cylindrical tanks has diameter =2m and length 4.2m
Cuboidal vessel has base area =3.96m
2
Cylindrical vessel has radius 1m
Amount of milk in cylindrical tanker will be equal ti its volume i.e. πr
2
h
⇒π(
2
d
)
2
h
⇒π(
2
2
)
2
(4.2)
=4.2πm
3
Now the cylindrical vessel is supplying milk in two booth in the ratio 3:2.
So amount of milk in cuboidal vessel is 2.52πm
3
and in cylindrical vessel is 1.68πm
3
Step 2: Calculating level of milk in cuboidal vessel
Now, amount of milk in cuboidal vessel will be equal to its volume.
So, volume of cuboid =(basearea)×height
2.52πm
3
=(3.96m
2
)×h
⇒h=1.99m
Therefore level of milk in cuboidal vessel is 1.99m.
Step 3: Calculating level of milk in cylidrial vessel
Now, amount of milk in cylindrical vessel will be equal to its volume.
So, volume of cyclindrical vessel =πr
2
h
⇒h=1.68m
Therefore, level of milk in cylindrical vessel is 1.68m
Hecen, level of milk in cuboidal and cylindrical vessel is 1.99m and 1.68m respectively.