Question

Each tennis ball is 2.63 inches in diameter. A sketch of the specially designed container is below. How many tennis balls can fit inside the container? How many more tennis balls could fit into the container if the container’s dimensions are doubled?

Answer 1

Ok let's find the volume of just the container

Answer 2

this is a combo of a cylinder (bottom) and a cone (on top)

Answer 3

so you need to find the volume of each piece, then add the two pieces to get the total volume

Answer 4

V of Cylinder= (3.14)(r^2)(h)
(3.14)(6.5^2)(36)
(3.14)(42.25)(36)
4775.94

Answer 5

good

Answer 6

now find the volume of the cone

Answer 7

V of cone= 1/3(3.14)(r^2)(h)
.3(3.14)(6.5^2)(8)
.3(3.14)(42.25)(8)
318.396

Answer 8

1/3 is 0.3 is approximate

0.33333 is a better approximation

If it were me, I'd just keep it as 1/3 and multiply it with (3.14)(42.25)(8)

Answer 9

Doing that gives

(1/3)*(3.14)(42.25)(8) = 353.773333333333

Answer 10

The combined volume of the two pieces is

4775.94+353.773333333333 = 5129.71333333333

So that's the approximate volume of the entire container

Answer 11

What is the volume of 1 tennis ball?

Answer 12

2.63 ?

Answer 13

You use the volume of a sphere formula

V = (4/3)*pi*r^3

Answer 14

The radius is 2.63/2 = 1.315

Answer 15

What would the height be?

Answer 16

of the tennis ball?

Answer 17

a sphere doesn't have a height really, but you can think of a sphere sitting on a flat surface

Answer 18

and the "height" is really the diameter of the sphere

Answer 19

never mind, I was thinking of the wrong formula lol, this is what I have so far:
V of ball =4/3 (3.14)(r)^2(h)
4/3 (3.14)(2.63^2)(h)
4/3 (3.14)(1.315^3)

Answer 20

2.63 is the diameter, not the radius

Answer 21

and you're using the cylinder volume formula (in a way)

Answer 22

it should be

Volume of a tennis ball

V = (4/3)*pi*r^3

V = (4/3)*(3.14)*(1.315)^3

V = ???

Answer 23

ya, I started to do that, I noticed after I asked for the height sorry

Answer 24

that's ok

Answer 25

V of ball =4/3 (3.14)(r)^2(h)
4/3 (3.14)( 1.315^2)(h)
4/3 (3.14)(1.315^3)
4/3 (3.14)(2.273930875)
4/3 (7.1401429475)
Can you finish it off with the fraction? I have trouble if its not a decimal.

Answer 26

I'd use a calculator to get (4/3)*(7.1401429475) = 9.52019059666667

Answer 27

If you are using a TI-83, you would type in exactly as you see it

Answer 28

I only have a simple calculator, it doesn't work like that. Btw what do we do now, Divide them just like in the other one you helped me with?

Answer 29

yes, divide the volume of the container by the volume of the ball

Answer 30

what do you get when you do so

Answer 31

5129.71333333333 / 9.52019059666667= 538.8246465495565

Answer 32

I'm getting 538.824646549557, so they're about the same

Answer 33

Round down to the nearest whole number: 538.824646549557 ---> 538

Answer 34

If you were able to melt down each tennis ball and pour all of that into the container, then you can fit up to 538 tennis balls. However, there's going to be empty space because the solid tennis balls cannot be altered in shape (very much). It's like the penny problem but a bit more complicated. So you're going to be able to fit (much) less than 538 tennis balls. I'd imagine you can fit more tennis balls in the cylinder portion than in the cone portion.

Answer 35

The last thing you need to do is answer the question "How many more tennis balls could fit into the container if the container’s dimensions are doubled?"

and you do so by following the same steps but the container will have everything doubled (the dimensions, NOT the volume). The tennis ball will stay the same volume

once you get this second result, you subtract off 538 to find the extra number of tennis balls you can store

Answer 36

I thought 538 would be the answer because it was between the solved problems???

Answer 37

There are 2 questions

How many tennis balls can fit inside the container?

How many more tennis balls could fit into the container if the container’s dimensions are doubled?

Answer 38

the 538 answers the first question

Answer 39

it's really the upper limit since (a lot) less can really fit in there

Answer 40

so 538 time 2?

Answer 41

not quite

Answer 42

you have to multiply each dimension in the pic by 2

Answer 43

then recompute the volume of the container

Answer 44

I'm sorry, I am a bit confused. so the problem would basically start from the beginning again, but doubled by 2?

Answer 45

or do we just 5129.71333333333 time 2 and 9.52019059666667 times 2???

Answer 46

yeah redo everything basically

Answer 47

but the radius is doubled, the height is doubled (for each piece)

Answer 48

the volume of the ball stays the same

Answer 49

like this?
V cyl= (3.14)(42.25*2)(36*2)
(3.14)(84.5)(72)
19103.76

Answer 50

no, the initial radius is 6.5

double that to get 2*6.5 = 13

the new radius is 13

Answer 51

the original height of the cylinder is 36 in

so the new height is 2*36 = 72 in

Answer 52

so you will plug r = 13, h = 72 into

V = pi*r^2*h

to find the volume of the new larger cylinder

Answer 53

It might help to draw it out