Question

A right cylindrical container perfectly holds 5 tennis balls placed one above the other. The radius of each ball is 3.35 centimeters. What is the approximate volume of the unoccupied space in the container? Use pi = 22 / 7

Answer 1

Hello there! To start, let's get the volume of each tennis ball. Do you know the volume formula for a sphere?

Answer 2

The volume is about 157.48

Answer 3

The formula is v = 4/3 pi r ^3

Answer 4

Correct, so do you have the volume of the cylinder as well?

Answer 5

That I do not

Answer 6

Would the radius be 3.35 for the cylinder too?

Answer 7

Correct. Your problem makes that part easy.

Answer 8

the height.. would I multiply the radius of the tennis balls by 5?

Answer 9

The volume for a cylinder is as follows:\[V = \pi r^2 h\]

Answer 10

So we know the radius, am I right about the height?

Answer 11

Or do we need to figure that out

Answer 12

We need the diameter, not the radius. That's an easy calculation, though.

Answer 13

6.7?

Answer 14

For each ball, yes. So multiply that by 5 to get the height.

Answer 15

33.5

Answer 16

Correct, now using that as height, input that with your radius into the volume formula above.

Answer 17

I got 1181.09?

Answer 18

Don't doubt yourself, you're correct. Note that that's the total volume of the cylinder containing the tennis balls. So let's take the total volume of each ball, as determined above, multiply that by 5, and subtract that from the the 1181.09 to get the empty space!

Answer 19

About 394 cm^3

Answer 20

Correct!

Answer 21

Thank you! Could you help me with another?

Answer 22

Sure.

Answer 23

Find the approximate volume of the cylinder shown in the diagram. Use pi = 22/7, and round your answer to the nearest integer value.

Answer 24

I suck at these, lol sorry

Answer 25

No worries, just give me a moment.

Answer 26

ok :)

Answer 27

Alright! Got it! For your own use, you may find this site very useful: http://goo.gl/A6Il02

Answer 28

Now, specifically, the site lists the formula for an oblique cylinder as \[V = hA(b)\] with the formula for A(b) being \[A(b) = \pi R^2\] Got it?

Answer 29

Yeah, okay

Answer 30

I know they're nothing simple, but taking it in steps makes it simple. What variables within the two formulas can we fill in right now?

Answer 31

the radius and height?

Answer 32

Yep. What are those?

Answer 33

R= 11
H= uhh 19?

Answer 34

Actually, I misspoke. We have to find the height, but that's a mere formula away! Do you recall the Pythagorean theorem?

Answer 35

Yes

Answer 36

The hypotenuse is easily known here, it's simply 19 (the slanted side). And we can gain the bottom value (what could be known as 'a') by taking the known radius, 11, and subtracting it from the bottom length of 19. What's that number?

Answer 37

8. But for the hypotenuse, do you mean 17 or 19?

Answer 38

The hypotenuse is 17cm, as given. Understand so far?

Answer 39

Yes. The height should be 15 then, right?

Answer 40

Exactly! (I really do appreciate you knowing how to solve formulas, you make my job really easy.) Now knowing h (15) and r (11), try to solve the question using the formulas above.

Answer 41

A(b)= 380.13

Is that correct?

Answer 42

Yep. Now multiply that by the height.

Answer 43

5701.95

Answer 44

Correct! And that's your final answer.

Answer 45

Awesome. Thank you again. You're a lifesaver! I might need help with another in a second if that's not too much trouble! I'll be sure to open a new question though so you can get the medal you deserve

Answer 46

Sure. Just mention me if I don't join immediately.

Answer 47

Alrighty :)