Math

QuestionA tank is 60 cm60 \mathrm{~cm} long, 50 cm50 \mathrm{~cm} wide, with 3 cubes of edge 10 cm10 \mathrm{~cm}. It fills at 10 L/min for 6 min. Find height.

Studdy Solution

STEP 1

Assumptions1. The tank is rectangular in shape with length60 cm and width50 cm. . The tank contains3 metal cubes each with an edge of10 cm.
3. The tank is being filled with water flowing from a tap at a rate of10 liters per minute.
4. It takes6 minutes to fill up the tank.
5. The tank is filled up to its brim.

STEP 2

First, we need to find the volume of water that fills the tank. We can do this by multiplying the rate of water flow by the time it takes to fill the tank.
Volumewater=FlowratetimesTimeVolume_{water} = Flow\, rate \\times Time

STEP 3

Now, plug in the given values for the flow rate and time to calculate the volume of water.
Volumewater=10liters/minutetimes6minutesVolume_{water} =10\, liters/minute \\times6\, minutes

STEP 4

Calculate the volume of water that fills the tank.
Volumewater=10liters/minutetimes6minutes=60litersVolume_{water} =10\, liters/minute \\times6\, minutes =60\, liters

STEP 5

We know that1 liter equals1000 cubic centimeters. So, we need to convert the volume of water from liters to cubic centimeters.
Volumewater=60literstimes1000cm3/literVolume_{water} =60\, liters \\times1000\, cm^3/liter

STEP 6

Calculate the volume of water in cubic centimeters.
Volumewater=60literstimes1000cm3/liter=60000cm3Volume_{water} =60\, liters \\times1000\, cm^3/liter =60000\, cm^3

STEP 7

The volume of water that fills the tank is equal to the volume of the tank minus the volume of the3 cubes. So, we need to find the volume of one cube and then multiply it by3.
Volumecube=edge3Volume_{cube} = edge^3

STEP 8

Plug in the given value for the edge to calculate the volume of one cube.
Volumecube=10cm3Volume_{cube} =10\, cm^3

STEP 9

Calculate the volume of one cube.
Volumecube=cm3=100cm3Volume_{cube} =\, cm^3 =100\, cm^3

STEP 10

Calculate the total volume of the3 cubes.
Volumecubes=3timesVolumecube=3times1000cm3=3000cm3Volume_{cubes} =3 \\times Volume_{cube} =3 \\times1000\, cm^3 =3000\, cm^3

STEP 11

The volume of the tank is equal to the volume of the water plus the volume of the cubes. So, we can find the volume of the tank.
Volumetank=Volumewater+VolumecubesVolume_{tank} = Volume_{water} + Volume_{cubes}

STEP 12

Plug in the values for the volume of water and the volume of the cubes to calculate the volume of the tank.
Volume_{tank} =60000\, cm^ +3000\, cm^

STEP 13

Calculate the volume of the tank.
Volumetank=60000cm3+3000cm3=63000cm3Volume_{tank} =60000\, cm^3 +3000\, cm^3 =63000\, cm^3

STEP 14

The volume of a rectangular tank is given by the product of its length, width, and height. So, we can find the height of the tank by dividing the volume of the tank by the product of its length and width.
Height=Volumetank/(LengthtimesWidth)Height = Volume_{tank} / (Length \\times Width)

STEP 15

Plug in the values for the volume of the tank, length, and width to calculate the height of the tank.
Height=63000cm3/(60cmtimes50cm)Height =63000\, cm^3 / (60\, cm \\times50\, cm)

STEP 16

Calculate the height of the tank.
Height=63000cm3/(60cmtimes50cm)=21cmHeight =63000\, cm^3 / (60\, cm \\times50\, cm) =21\, cmThe height of the tank is21 cm.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord