A farmer connects a pipe of …

According to question,A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field, which is 10 m in diameter and 2 m deep.

Diameter of pipe = 20 cm.

{tex} \therefore{/tex} Radius of pipe {tex} = \frac { 20 } { 2 } = 10 \mathrm { cm }{/tex}

{tex}= 0.10 m{/tex}

Diameter of tank = 10 m

{tex}\therefore{/tex} radius of the tank {tex}= \frac { 20 } { 2 } = 5 \mathrm { m }{/tex}

Depth of tank = 2m

Volume of tank {tex}= \pi r ^ { 2 } h{/tex}

{tex}= \pi \times 5 \times 5 \times 2{/tex}

{tex}= 50 \pi{/tex}

Speed of the water 3 km/ hr.

{tex}= \frac { 3000 } { 60 } = 50 \mathrm { m } / \mathrm { min }{/tex}

Volume of water supplied in one minute

{tex}= \pi r ^ { 2 } h{/tex}

{tex}= \pi \times 0.10 \times 0.10 \times 50{/tex}

Let time taken by {tex}t = \frac { 50 \pi } { \pi \times .10 \times 0.10 \times 50 } = 100{/tex}

Hence time taken to fill the tank = 100 minutes.