A dispenser holds 5652 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 4239 cm3 of soap remains in the dispenser? Use 3.14 to approximate pi.

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07-01-2016
Mathematics

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A dispenser holds 5652 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 4239 cm3 of soap remains in the dispenser? Use 3.14 to approximate pi.

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taskmasters taskmasters · Answer 1 · 2016-01-07T16:04:24+01:00

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