Question

@ganeshie8 Challenge #2 — Tennis Trouble:

Now it's time to move on to the second challenge called Tennis Trouble. The second challenge is to figure out how many tennis balls fit in a specially designed container. The radio station will give away a prize pack and a pair of front row tickets to the winner of this challenge! 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

find the volume of tennis ball
find the volume of container

divide

Answer 2

`Each tennis ball is 2.63 inches in diameter.`

Diameter = 2.63,
that means radius = ?

Answer 3

1.315

Answer 4

yes, whats the volume of a sphere of radius 1.315 ?

Answer 5

Volume of sphere = V = 4/3 * pi * r^3 so

V = 4/3 * 3.14 * 1.315^3 = 9.52019

Answer 6

save it,
find the volume of given container

Answer 7

Notice that its a composition of two shapes :
1) cylinder in the bottom
2) cone in the top

Answer 8

find the volume of each shape and add up

Answer 9

its a cylinder so

v = pi * r^2 * h
v = 3.14 * 6.5 * 36

correct ?

Answer 10

Correct !
find the volume of top cone also

Answer 11

volume of cylinder is 734.76

Answer 12

Volume of cone
V = 1 over 3 (πr2)(h)

Answer 13

oh wait i did it wrong

Answer 14

for the cylinder the answer is 4775.94 right ?

Answer 15

volume of cylinder is 734.76
is correct

Answer 16

what are the dimensions of cone ?
radius = ?
height = ?

Answer 17

wait but i didnt do the squared part..

Answer 18

6.5 ^ 2

Answer 19

Oops! yes

Answer 20

4775.94 is correct volume for bottom cylinder
http://www.wolframalpha.com/input/?i=3.14*6.5%5E2*36

Answer 21

radius of cone is 6.5 and height is 8

Answer 22

yep! find the volume

Answer 23

353.773 ?

Answer 24

sorry... OS is lagging -_-

Answer 25

@ganeshie8

Answer 26

@johnweldon1993

Answer 27

Yes that is the correct volume for the cone on top (I got a slightly different number but I assume you used 3.14 for pi)

So the volume of the total composite figure will be the sum of our 2 volumes

\[\large \text{Total Volume} = \text{Volume of Cylinder} + \text{Volume of Cone}\]
\[\large V = 4775.94 + 353.773 = ?\]

Answer 28

And then, since we now know the total volume, we divide that by the volume of a single tennis ball to figure out how many can fit inside.

Answer 29

Okay, the volume of a cylinder as it is originally would is

\[\large \pi r^2 h\] correct?

if we were to double the dimensions of this cylinder (double the radius and the height) we would have

\[\large \pi (2r)^2 2h\]
\[\large \pi 4r^22h\]
\[\large 8\pi r^2 h\]

So this means if we double the dimensions of our cylinder, the volume will increase by a factor of 8

Answer 30

And for the cone...same idea

\[\large V = \frac{\pi r^2h}{3}\]

if we double the dimensions (again the radius and the height) we have

\[\large V = \frac{\pi (2r)^2 2h}{3}\]
\[\large V = \frac{\pi 4r^2 2h}{3}\]
\[\large V = 8\frac{\pi r^2h}{3}\]

so again with the cone as well, if we double the dimensions of it, we will increase the volume by a factor of 8.

Answer 31

So all we need to do, is multiply the volume we received for the cylinder by 8....and then multiply the volume of the cone by 8...and then add the results

Answer 32

ty soo much!

Answer 33

Anytime :)