Question

A cylindrical room is filling with water. Currently, it is ⅓ full. The water is flowing into the room at a rate of 14𝝅 m³ per minute. How many minutes do the thieves have to escape by opening the exit door before the room is completely filled with water?

• A. 3 minutes
• B. 7 minutes and 15 seconds
  
• C. 6 minutes
• D. 4 minutes and 30 seconds

Answer 1

The correct option is A 3 minutes

Radius of cylindrical room = 3 m

Height of the room = 7 m

Volume of the room = $\pi$ ${\text{r}}^2$ h
= $\pi$ $\times$ 3 $\times$ 3 $\times$ 7
= 63$\pi$ ${\text{m}}^3$

Room is already 1/3rd full.
i.e. $\frac{63\pi }{3}$ = 21$\pi$ ${\text{m}}^3$
Remaining capacity of the room:
63$\pi$ - 21$\pi$

= 42$\pi$ ${\text{m}}^3$

Rate of flow of water = 14$\pi$ ${\text{m}}^3$

Therefore,

Time do the thieves have to escape:

= $\frac{42\pi }{14\pi }$

= 3 minutes


Option a will be the answer.