Question #148400
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=πr2hV = \pi r^2 h .

Knowing that r=d2r=\frac{d}{2} we can write the formula as V=π(d2)2hV = \pi (\frac{d}{2})^2 h .

The following statements are given:

V1=V2=121000cm3V_1=V_2=12 * 1000 cm^3

h1=2d1h_1=2d_1

h2=3d2h_2=3d_2

We can write the following equation for the first cylinder:

V1=π(d12)2h1V_1=\pi (\frac{d_1}{2})^2 h_1

121000cm3=π(d12)22d112 * 1000cm^3=\pi (\frac{d_1}{2})^2 2d_1

12000cm3=π(d1)3212000cm^3=\pi \frac{(d_1)^3}{2}

d1=12000cm32π3d_1 = \sqrt[3]{\frac{12000cm^3*2}{\pi}}

d119.695cmd_1 \approx 19.695 cm

We can write the following equation for the second cylinder:

V2=π(d22)2h2V_2=\pi (\frac{d_2}{2})^2 h_2

121000cm3=π(d22)23d212 * 1000cm^3=\pi (\frac{d_2}{2})^2 3d_2

12000cm3=π3(d2)3412000cm^3=\pi \frac{3(d_2)^3}{4}

d2=12000cm343π3d_2 = \sqrt[3]{\frac{12000cm^3*4}{3\pi}}

d217.205cmd_2 \approx 17.205 cm

The answers to the given parts of the question are 19.69519.695 and 17.20517.205, respectively.


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