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Question
Below are the drawings of cross sections of two different pipes used to fill swimming pools. Figure A is a combination of 2 pipes each having a radius of 8 cm. Figure B is a pipe having a radius of 15 cm. If the force of the flow of water coming out of the pipes is the same in both the cases, which will fill the swimming pool faster?
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Solution
In figure A, 2 pipes each having a radius of 8 cm
∵ Area of a circle = πr2
∴ Area of one pipe = `22/7 xx 8 xx 8`
= `(22 xx 8 xx 8)/7`
= `(22 xx 64)/7` cm2
Area of 2 pipes = `(2 xx 1408)/7`
= `2816/7` cm2
= 402.28 cm2
In figure B, a pipe having radius of 15 cm
∴ Area of the pipe = πr2
= `22/7 xx 15 xx 15`
= `22/7 xx 225`
= `4950/7`
= 707.14 cm2
Clearly, the surface area of pipe B is greater. So, pipe B fills the swimming pool faster.
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