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.
______________________ What is the diameter of the first container in cm?
_______________________ What is the diameter of the second container in cm?
1
Expert's answer
2020-12-04T12:03:34-0500
The volume of a cylinder is V=πr2h .
Knowing that r=2d we can write the formula as V=π(2d)2h .
The following statements are given:
V1=V2=12∗1000cm3
h1=2d1
h2=3d2
We can write the following equation for the first cylinder:
V1=π(2d1)2h1
12∗1000cm3=π(2d1)22d1
12000cm3=π2(d1)3
d1=3π12000cm3∗2
d1≈19.695cm
We can write the following equation for the second cylinder:
V2=π(2d2)2h2
12∗1000cm3=π(2d2)23d2
12000cm3=π43(d2)3
d2=33π12000cm3∗4
d2≈17.205cm
The answers to the given parts of the question are 19.695 and 17.205, respectively.
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