Question

Question 104

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?

Answer 1

In figure A, 2 pipes each having a radius of 8 cm
$\therefore$ Area of a circle $=\pi r^2$
$\therefore$ Area of one pipe $=\frac{22}{7}\times 8\times 8$
$=\frac{22\times 8\times 8}{7}=\frac{22\times 64}{7}c{m}^2$
Area of 2 pipes $=\frac{2\times 1408}{7}=\frac{2816}{7}c{m}^2=402.28c{m}^2$
In figure B, a pipe having radius of 15 cm
$\therefore$ Area of the pipe $=\pi r^2$
$=\frac{22}{7}\times 15\times 15=\frac{22}{7}\times 225=\frac{4950}{7}=707.14c{m}^2$
Clearly, the surface area of pipe B is greater. So, pipe B fills the swimming pool faster.