Question #140042
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?
1
Expert's answer
2020-10-25T19:05:25-0400

Explanations & Calculations


  • It should be known that the volume (V) of a cylinder is given by, V=πr2h\small V = \pi r^2h : r is the radius of the base surface.
  • Now the data is given for the diameter which is 2×\small 2\times radius. Therefore, the radius is r=d2r =\large \frac{d}{2}
  • And the volume should be expressed in cm3\small cm^3 because the algebraic expression is written with lengths.
  • Therefore,

V=π(d2)2h=12×1000cm3πd24×2d=12×1000cm3d=120000×2πcm33=19.695cm\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}



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