NTSE Stage 2 SAT 2018 Exam Question Paper

Question : 50 of 100

Marks: +1, -0

The surface of water in a swimming pool, when it is full of water, is rectangular with length and breadth 36 m and 10.5 m respectively. The depth of water increases uniformly from 1m at one end to 1.75 m at the other end. The water in the pool is emptied by cylindrical pipe of radius 7 cm at the rate of 5 km/h. The time (in hours) to empty water in the pool is (take

π=22/7

)

$61/4$
$61/2$
$63/4$
$64/5$

Validate

Solution:

Let r be the radius of cylindrical pipe
Then,

r=7{cm}=\;\;{7}/{100}{m}

Volume of water in swimming pool
= Area of cross section × Speed × Time

[\;\;{1}/{2}(1+1.75)×36]×10.5=πr^{2}×\;\text"speed"\;×\text "time"

[\;\;{1}/{2}(1+1.75)×36]10.5=\;\;{22}/{7}×\;\;{7}/{100}×\;\;{7}/{100}×5000×t

t=\;\;{27}/{4}=6\;\;{3}/{4}

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