A cylindrical container of height equal to twice the diameter of its base can
hold 12 liters (1L= 1,000 cm3) of water. Another cylindrical container with
the same capacity has its height equal to three times the diameter of its
base.
1.What is the diameter of the second container?
1
Expert's answer
2020-11-16T08:31:33-0500
Let d1= the diameter of the base of the first container, h1= the heigth of the first container and V1= the volume of the first container.
Let d2= the diameter of the base of the second container, h2= the heigth of the second container and V2= the volume of the second container.
Then
h1=2d1,V1=π(2d1)2h1=21πd13=161πh13
h2=3d2,V1=π(2d2)2h2=43πd23=361πh23
Given
V1=V2=12L=12000cm3
43πd23=12000cm3
d2=33π4(12000)cm
d2=203π2cm≈17.205cm
The diameter of the second container is 203π2cm≈17.205cm.
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