12.6 Strategy for Composite Solids

1. Pipe Volume (Input): Radius $r = 1$ cm. Speed = 80 cm/sec. Time = 30 mins = 1800 sec.

Length of water column = Speed $\times$ Time = $80 \times 1800 = 144000$ cm.

Volume In = $\pi r^2 L = \pi (1)^2 (144000) = 144000\pi$ cm³.

2. Tank Volume (Output): Radius $R = 40$ cm. Let rise be $H$.

Volume Out = $\pi R^2 H = \pi (40)^2 H = 1600\pi H$.

3. Equate: $1600\pi H = 144000\pi$.

4. Solve: $H = 144000 / 1600 = 1440 / 16 = 90$ cm.