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?
Solution:
Since the speed of the flow of water through all the pipes is same the amount of water flowing out of these pipes will depend on the cross sectional area of the pipes.which depends on the radius of the pipes.
The joint area of the pipes in figure A is:
= πr² + πr²
= π(8)² + π(8)²
= 64π + 64π
= 128πcm²
The area of pipe in figure B will be
= πR²
= π(15)²
= 225πcm²
Since the rate at which the water is flowing is same and the area of pipe in Figure B is more than the area of pipes in Figure A the pipe in pipe in figure B will fill the swimming pool faster.
✦ Try This: 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 12 cm. Figure B is a pipe having a radius of 16 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?
Since the speed of the flow of water through all the pipes is same the amount of water flowing out of these pipes will depend on the cross sectional area of the pipes.which depends on the radius of the pipes.
The joint area of the pipes in figure A is:
= πr² + πr²
= π(12)² + π(12)²
= 144π + 144π
= 288πcm²
The area of pipe in figure B will be
= πR²
= π(16)²
= 256πcm²
Since the rate at which the water is flowing is same and the area of pipes in Figure A is more than the area of pipes in Figure B the pipe in pipes in figure A will fill the swimming pool faster.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Problem 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?
Summary:
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, then pipe in figure B i.e. pipe with radius 15cm will fill the swimming pool faster
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