Problem solving

[Starfish]

A circular pool has a diameter of 3m and is filled to a depth of 70cm. Mr Thorpe climbs into the pool and submerges for ten seconds while his son measures the new depth at 72cm. Calculate Mr Thorpe's volume

3~r @70cm = 659.7344573 3~r@72cm = 678.5840132 I have subtracted large number from small to get 18.4955589cm3 and rounded to 18.85 cm3 (3dp)

Can you tell me where I have gone wrong?????

Help!!!

 

[tkhunny]

It appears to me that you probably should use the radius, rather than the diameter, when calculating the volume of the pool.

 

[lookagain]

It appears to me that you probably should use the radius, rather than the diameter,
when calculating the volume of the pool.

Also, Starfish, you have to have all of the dimensions in terms of the same unit.

For example, have all of the dimensions in terms of centimeters, or have all of them in terms of meters.


I'll use meters:

The radius is \(\displaystyle 1.5 \ meters.\)

The original depth (height of a cylinder) is \(\displaystyle 0.70 \ meter.\)

The new depth (height of a cylinder) is \(\displaystyle 0.72 \ meter.\)


\(\displaystyle Volume \ (of \ the \ cylindrical \ pool) \ = \ \pi r^2 h\)


\(\displaystyle New \ volume \ - old \ volume \ = \\)


\(\displaystyle \pi (1.5 \ m.)^2 (0.72 \ m.) \ - \ \pi(1.5 \ m.)^2(0.70 \ m.) =\)

\(\displaystyle \pi (1.5 \ m.)^2 (0.02 \ m.) \approx \ 0.141372 \ cubic \ meter \ \approx \ \frac{1}{7} \ cubic \ meter\)


\(\displaystyle Then \ Mr. \ Thorpe's \ volume \ is \ about \ 0.141372 \ m.^3\)