Answer to Question #148400 in Trigonometry for yui

Question

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?

Answer 1

The volume of a cylinder is $V = \pi r^2 h$ .

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

The following statements are given:

$V_1=V_2=12 * 1000 cm^3$

$h_1=2d_1$

$h_2=3d_2$

We can write the following equation for the first cylinder:

$V_1=\pi (\frac{d_1}{2})^2 h_1$

$12 * 1000cm^3=\pi (\frac{d_1}{2})^2 2d_1$

$12000cm^3=\pi \frac{(d_1)^3}{2}$

$d_1 = \sqrt[3]{\frac{12000cm^3*2}{\pi}}$

$d_1 \approx 19.695 cm$

We can write the following equation for the second cylinder:

$V_2=\pi (\frac{d_2}{2})^2 h_2$

$12 * 1000cm^3=\pi (\frac{d_2}{2})^2 3d_2$

$12000cm^3=\pi \frac{3(d_2)^3}{4}$

$d_2 = \sqrt[3]{\frac{12000cm^3*4}{3\pi}}$

$d_2 \approx 17.205 cm$

The answers to the given parts of the question are $19.695$ and $17.205$, respectively.