A garden hose of circular cross-section has an internal diameter of

MATHEMATICS · Multi-part · GCSE · Mathematics · Geometry and Measures · Geometry and Measures

Problem

2.0\,\text{cm}

. Water exits the hose at a uniform speed of

3.0\,\text{m}\,\text{s}^{-1}

and is used to fill an empty circular wading pool that has an inner radius of

2.5\,\text{m}

and a uniform depth of

1.0\,\text{m}

. Ignore any splashing losses. (a) Calculate the total volume of water required to completely fill the pool. (b) Determine the volume flow rate of water leaving the hose. (c) Using your results from parts (a) and (b), calculate the time, in hours, required to fill the pool. (d) The homeowner mistakenly believes that doubling the exit speed of the water would halve the filling time. Using proportional reasoning based on your calculations, evaluate this claim.

Related theory

Dimensional Analysis
Ratio and Proportion
Volume of Solids
Mensuration

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