Answer to Question #140042 in Geometry for ZXCVC

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.
1. What is the diameter of the first container?

Answer 1

Explanations & Calculations

• It should be known that the volume (V) of a cylinder is given by, $\small V = \pi r^2h$ : r is the radius of the base surface.
• Now the data is given for the diameter which is $\small 2\times$ radius. Therefore, the radius is $r =\large \frac{d}{2}$
• And the volume should be expressed in $\small cm^3$ because the algebraic expression is written with lengths.
• Therefore,

$\qquad\qquad \begin{aligned} \small V &= \small \pi \Big(\frac{d}{2}\Big)^2h = 12\times 1000cm^3\\ \small \pi \frac{d^2}{4}\times 2d&=\small 12\times 1000cm^3\\ \small d &= \small \sqrt[3]{\frac{120000\times 2}{\pi} cm^3}\\ &= \small \bold{19.695cm} \end{aligned}$