bigrome10
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A cylinder shaped dispenser holds 5,652 cm³ of liquid soap and is now full. The radius of the dispenser is 7.5 cm. What is the difference between the height of the soap in the full dispenser and the height when 4,239 cm³ of soap remains in the dispenser? Use 3.14 to approximate pi.

Verified Answer :

Dave1357

30cm is the difference between the height of the soap in the full dispenser and height of the remaining soap. 

The formula for cylindrical height is: 

  Area
  --------     -  r
2  π r

Cylindrical height of full dispenser.

      5652                            5652
---------------------   - 7.5    =  ------------  - 7.5  =  120 - 7.5 = 112.50
2 3.14 7.5                     47.1

Cylindrical height of dispenser with lesser liquid soap 
     
     4239                       4239
--------------------  - 7.5 =  ------------  - 7.5 = 90 - 7.5 = 82.50
2 3.14 7.5                47.1


Cylindrical height of full soap                112.50
Cylindrical height of lesser soap           - 82.50 
Difference in height of soap content       30.00 

Hope it helps! :D

Here, Just need to apply the formula of "Volume of Cylinder"
We know, Volume of a Cylinder = πr²h

In 1st condition (when dispenser is full), 
5652 = 3.14 7.5² h₁
5652 = 176.625 h₁
h₁ = 5652/176.625
h₁ = 32 cm

Now, In 2nd Condition (when dispenser is not fulled), 
4239 = 3.14 7.5² h₂
4239 = 176.625 h₂
h₂ = 4239 / 176.625
h₂ = 24 cm

Now, Difference = h₁ - h₂
Δh = 32 - 24 = 8 cm

In short, Your Final Answer would be 8 cm

Hope this helps!

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