text: 1
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  # Water is flowing into a vertical cylindrical tank of radius 2 ft at the rate of 8 cubic/minute. The rate at which the water level is rising, is _______________.
  
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  ## Let h be the water level in the cylindrical tank at time t minutes. Radius of the cylinder, r = 2 ft ∴ Volume of the water in the cylindrical tank at time t, V = $\mathrm{\pi }{r}^{2}h$ = $\mathrm{\pi }×{\left(2\right)}^{2}×h$ $V=4\mathrm{\pi }h$ Differentiating both sides with respect to t, we get $\frac{dV}{dt}=4\mathrm{\pi }×\frac{dh}{dt}$ Now, $\frac{dV}{dt}$ = 8 cubic feet/minute (Given) $\therefore 8=4\mathrm{\pi }×\frac{dh}{dt}$ $⇒\frac{dh}{dt}=\frac{8}{4\mathrm{\pi }}=\frac{2}{\mathrm{\pi }}$ ft/min Thus, the water level in the tank is rising at the rate of $\frac{2}{\mathrm{\pi }}$ feet/minute. Water is flowing into a vertical cylindrical tank of radius 2 ft at the rate of 8 cubic/minute. The rate at which the water level is rising, is $\overline{)\frac{2}{\mathrm{\pi }}\mathrm{feet}/\mathrm{minute}}$.
  
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explanation: The document contains a math question and its corresponding solution. The question asks for the rate at which the water level is rising in a cylindrical tank given the flow rate and the radius of the tank. The solution is provided, showing the step-by-step calculation to determine the rate of rise of the water level.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: 1
  You visited us 1 times! Enjoying our articles? Unlock Full Access!
  Question
  
  # Water is flowing into a vertical cylindrical tank of radius 2 ft at the rate of 8 cubic/minute. The rate at which the water level is rising, is _______________.
  
  Open in App
  Solution
  
  ## Let h be the water level in the cylindrical tank at time t minutes. Radius of the cylinder, r = 2 ft ∴ Volume of the water in the cylindrical tank at time t, V = $\mathrm{\pi }{r}^{2}h$ = $\mathrm{\pi }×{\left(2\right)}^{2}×h$ $V=4\mathrm{\pi }h$ Differentiating both sides with respect to t, we get $\frac{dV}{dt}=4\mathrm{\pi }×\frac{dh}{dt}$ Now, $\frac{dV}{dt}$ = 8 cubic feet/minute (Given) $\therefore 8=4\mathrm{\pi }×\frac{dh}{dt}$ $⇒\frac{dh}{dt}=\frac{8}{4\mathrm{\pi }}=\frac{2}{\mathrm{\pi }}$ ft/min Thus, the water level in the tank is rising at the rate of $\frac{2}{\mathrm{\pi }}$ feet/minute. Water is flowing into a vertical cylindrical tank of radius 2 ft at the rate of 8 cubic/minute. The rate at which the water level is rising, is $\overline{)\frac{2}{\mathrm{\pi }}\mathrm{feet}/\mathrm{minute}}$.
  
  Suggest Corrections
  1
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distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and its corresponding solution. The question asks for the rate at which the water level is rising in a cylindrical tank given the flow rate and the radius of the tank. The solution is provided, showing the step-by-step calculation to determine the rate of rise of the water level.
  
  Label: question-and-answer