Question

A swimming pool is circular with a 20-ft diameter. The depth is constant along east-west lines and increases linearly from 1 ft at the south end to 6 ft at the north end. Find the volume of water in the pool. (Round your answer to the nearest whole number.) ft3

Answer 1

Answer:

$1100 \text{feet}^3$

Step-by-step explanation:

GIVEN: A swimming pool is circular with a $20\text{ feet}$ diameter. The depth is constant along east-west lines and increases linearly from $1\text{ feet}$ at the south end to $6\text{ feet}$ at the north end.

TO FIND: Find the volume of water in the pool.

SOLUTION:

Consider the image attached.

when two similar figures are attached a new cylinder is formed. volume of swimming pool is half of volume of new cylinder formed.

radius of new cylinder $=\frac{\text{diameter}}{2}=\frac{20}{2}=10\text{ feet}$

height of new cylinder $=6+1=7\text{ feet}$

volume of cylinder $=\pi r^2h=\frac{22}{7}\times(10)^27$

                               $=2200\text{ feet}^3$

Volume of swimming pool $=\frac{\text{volume of cylinder}}{2}=\frac{2200}{2}$

                                           $=1100\text{ feet}^3$

Hence volume of water in the pool is $1100 \text{feet}^3$.