OpenStudy (anonymous):

A cylindrical tank with diameter 20 in. is half filled with water. How much will the water level rise if you place a metallic ball with radius of 4 in. in the tank? Give your answer to the nearest tenth. - What causes the water level in the tank to rise? - Which volume formulas should you use?

4 years ago
OpenStudy (anonymous):

pleeeease help

4 years ago
OpenStudy (austinl):

You have the volume of a cylinder. \[V_{cylinder} = \pi r^2 h\] The volume of a sphere. \[v_{sphere} = \frac{4}{3} \pi r^3\]

4 years ago
OpenStudy (anonymous):

So I find the volume of the cylinder and the volume of the sphere and subtract them, right? But, how would I find the volume of the cylinder if I'm not given the height?

4 years ago
OpenStudy (austinl):

No, add.

4 years ago
OpenStudy (anonymous):

I'm still confused.. what do I do about the height?

4 years ago
OpenStudy (austinl):

@amistre64

4 years ago
OpenStudy (ybarrap):

The tank will rise according to the new volume in the cylinder: $$ \Large V_{old} = \pi r_{cyl}^2h_{old}\\ \Large V_{new} = \pi r_{cyl}^2h_{old}+ \frac 4 3 \pi r_{ball}^3=\pi r_{cyl}^2h_{new}\\ \Large \implies \pi r_{cyl}^2h_{new} - \pi r_{cyl}^2h_{old}=\frac 4 3 \pi r_{ball}^3\\ \Large \implies h_{new}-h_{old}={\frac 4 3 \pi r_{ball}^3 \over \pi r_{cyl}^2}\\ \Large ={4 ~r_{ball}^3 \over 3 ~r_{cyl}^2} $$ Let me know if you have any questions.

4 years ago
OpenStudy (anonymous):

Am I just missing something super simple? What is the height?

4 years ago
OpenStudy (amistre64):

how high is "half filled with water" to begin with?

4 years ago
OpenStudy (amistre64):

you cannot determine the half volume of the cylindar without knowing how high it is to start with

4 years ago
OpenStudy (austinl):

That is where I got thrown and called in the cavalry(you @amistre64 )

4 years ago
OpenStudy (jdoe0001):

heheh

4 years ago
OpenStudy (anonymous):

It doesn't say in the book, it just says half filled with water

4 years ago
OpenStudy (jdoe0001):

@kaileylol can you post a quick screenshot?

4 years ago
OpenStudy (amistre64):

|dw:1377639096023:dw|

4 years ago