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Surface Areas and Volumes
RD Sharma
CBSE
Grade 10

Question:

A hemispherical tank full of water is emptied by a pipe at the rate of $3\dfrac{4}{7}$ litres per second. How much time will it take to empty half the tank, if it is $3\text{ m}$ in diameter?

Step-by-Step Solution

Key Concept: $r = 1.5\text{ m} = 3/2\text{ m}$. Half Tank Vol $= \dfrac{1}{2} \times \dfrac{2}{3} \times \dfrac{22}{7} \times \dfrac{27}{8} = \dfrac{99}{14}\text{ m}^3 = \dfrac{99000}{14}\text{ litres}$. Rate $= 25/7\text{ litres/sec}$. Time $= \dfrac{99000/14}{25/7} = \dfrac{99000}{50} = 1980\text{ sec} = 33\text{ minutes}$.
Half Tank Vol $= \dfrac{1}{3} \times \dfrac{22}{7} \times \dfrac{27}{8} = \dfrac{99}{14}\text{ m}^3 = \dfrac{99000}{14}\text{ litres}$. [1.5 Marks]
Time $= \dfrac{99000/14}{25/7} = \dfrac{99000}{50} = 1980\text{ seconds} = 33\text{ minutes}$. [1.5 Marks]

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🎯 Official CBSE Marking Scheme:
Calculating half tank volume in litres $= 99000/14$: 1.5 Marks
Evaluating time $= 1980\text{ sec} = 33\text{ minutes}$: 1.5 Marks

Correct Answer:
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