All of the water from a full cylinder tank is drained into a rectangular aquarium. The cylinder has a height of 50 cm and a diameter of 30 cm. How deep is the water in the aquarium, if it has a rectangular base measuring 40 cm by 20 cm?
All of the water from a full cylinder tank is drained into a rectangular aquarium. The cylinder has a height of 50 cm and a diameter of 30 cm. How deep is the water in the aquarium, if it has a rectangular base measuring 40 cm by 20 cm?
A cylinder with radius r units and height h units
has a volume of V cubic units given by
Vcylinder tank=π⋅r2⋅h=π⋅302⋅50 cm3=45000⋅π cm3=141371.669412 cm3
Vaquarium=a⋅b⋅h=40 cm⋅20 cm⋅h=800 cm2⋅h
Vcylinder tank=Vaquarium141371.669412 cm3=800 cm2⋅haquariumhaquarium=141371.669412 cm3800 cm2haquarium=176.714586764 cm
The water in the aquarium is 176.7 cm deep.
Or in meters: 1.767 m
This is an ORIGINAL VOLUME = FINAL VOLUME problem
Original volume pi x d x h = pi x 30 x 50 =4712.39 cm^3
This is also the FINAL VOLUME (though it is in a different shape!)
40 x 20 x h = 4712.39
h = 4712.39/ (40 x 20) = 5.89 cm deep
All of the water from a full cylinder tank is drained into a rectangular aquarium. The cylinder has a height of 50 cm and a diameter of 30 cm. How deep is the water in the aquarium, if it has a rectangular base measuring 40 cm by 20 cm?
A cylinder with radius r units and height h units
has a volume of V cubic units given by
Vcylinder tank=π⋅r2⋅h=π⋅302⋅50 cm3=45000⋅π cm3=141371.669412 cm3
Vaquarium=a⋅b⋅h=40 cm⋅20 cm⋅h=800 cm2⋅h
Vcylinder tank=Vaquarium141371.669412 cm3=800 cm2⋅haquariumhaquarium=141371.669412 cm3800 cm2haquarium=176.714586764 cm
The water in the aquarium is 176.7 cm deep.
Or in meters: 1.767 m