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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?

 Jan 21, 2016

Best Answer 

 #2
avatar+26397 
+10

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=πr2h=π30250 cm3=45000π cm3=141371.669412 cm3 

 Vaquarium=abh=40 cm20 cmh=800 cm2h 

 Vcylinder tank=Vaquarium141371.669412 cm3=800 cm2haquariumhaquarium=141371.669412 cm3800 cm2haquarium=176.714586764 cm 

 

The water in the aquarium is 176.7 cm deep.

Or in meters: 1.767 m

 

laugh 

 Jan 21, 2016
 #1
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+5

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

 Jan 21, 2016
 #2
avatar+26397 
+10
Best Answer

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=πr2h=π30250 cm3=45000π cm3=141371.669412 cm3 

 Vaquarium=abh=40 cm20 cmh=800 cm2h 

 Vcylinder tank=Vaquarium141371.669412 cm3=800 cm2haquariumhaquarium=141371.669412 cm3800 cm2haquarium=176.714586764 cm 

 

The water in the aquarium is 176.7 cm deep.

Or in meters: 1.767 m

 

laugh 

heureka Jan 21, 2016

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