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The rain water from a roof 22 m × 20 m drains into a conical vessel having a base of
diameter 2 m and height 3.5 cm. If the vessel is just full, find the rainfall in mm.

Asked by shailesh.solanki 18th March 2018, 7:35 PM
Answered by Expert
Answer:
begin mathsize 16px style Given colon
Dimension space of space roof space equals space 22 cross times 20
daimeter space of space straight a space conical space vessel space equals space 2 straight m
Therefore space radius space of space conical space vessel space equals space 2 over 2 space equals 1 straight m
height space of space straight a space conical space vessel space space equals space 3.5 straight m
Let space straight d space be space the space depthness space of space rain space water.
Therefore
Volume space of space rain space water space equals space Volume space of space conical space vessel
Here comma
Volume space of space rain space water space equals 22 space cross times space 20 space cross times space straight d
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 440 space cross times space straight d................ straight i right parenthesis
Volume space of space conical space vessel space equals space 1 third πr squared straight h
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 third cross times 22 over 7 cross times 1 cross times 1 cross times 3.5
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 11 over 3 straight m cubed.............. ii right parenthesis
from space straight i right parenthesis space and space ii right parenthesis
440 cross times straight d space equals space 11 over 3
Therefore space straight d space equals 1 over 120 space equals 0.008 straight m space equals space 0.008 space cross times 1000 space equals 8 mm space space space space space space space space space space space left parenthesis space 1 straight m space equals 100 cm space and space 1 cm space equals 10 mm space therefore space 1 straight m space equals 1000 mm space right parenthesis space
Hence space the space rainfall space is space 8 mm.
end style
Answered by Expert 19th March 2018, 10:45 AM
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