Question

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?

Answer 1

pleeeease help

Answer 2

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

Answer 3

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?

Answer 4

No, add.

Answer 5

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

Answer 6

@amistre64

Answer 7

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.

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

heheh

Answer 13

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

Answer 14

@kaileylol can you post a quick screenshot?

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