Answer to Question #144254 in Geometry for Dayana

Question #144254
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=d_1= the diameter of the base of the first container, h1=h_1= the heigth of the first container and V1=V_1= the volume of the first container.

Let d2=d_2= the diameter of the base of the second container, h2=h_2= the heigth of the second container and V2=V_2= the volume of the second container.

Then

h1=2d1,V1=π(d12)2h1=12πd13=116πh13h_1=2d_1, V_1=\pi (\dfrac{d_1}{2})^2h_1=\dfrac{1}{2}\pi d_1^3=\dfrac{1}{16}\pi h_1^3


h2=3d2,V1=π(d22)2h2=34πd23=136πh23h_2=3d_2, V_1=\pi (\dfrac{d_2}{2})^2h_2=\dfrac{3}{4}\pi d_2^3=\dfrac{1}{36}\pi h_2^3

Given


V1=V2=12L=12000cm3V_1=V_2=12L=12000cm^3

34πd23=12000cm3\dfrac{3}{4}\pi d_2^3=12000cm^3

d2=4(12000)3π3cmd_2=\sqrt[3]{\dfrac{4(12000)}{3\pi}}cm

d2=202π3cm17.205 cmd_2=20\sqrt[3]{\dfrac{2}{\pi}}cm\approx 17.205\ cm

The diameter of the second container is 202π3cm17.205 cm.20\sqrt[3]{\dfrac{2}{\pi}}cm\approx 17.205\ cm.



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