Question

A funnel with a height of 3.56 inches is shown below.
The funnel has a diameter of 1.38 inches that includes a wall that is 0.125 inches thick. What is the maximum volume of the funnel?

Answer 1

@jim_thompson5910

Answer 2

The idea here is to find the volumes of the two cones

Answer 3

Do you know how to do that?

Answer 4

no

Answer 5

The volume of any cone with radius 'r' and height h is

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

Answer 6

So what is the radius of the larger cone?

Answer 7

3.56?

Answer 8

no that's the height of both cones

Answer 9

is the radius given?

Answer 10

yes

Answer 11

well sort of...the diameter is given

Answer 12

the radius is half the diameter, so you just take half of 1.38 to get the radius

Answer 13

.69

Answer 14

yes

Answer 15

So that's the radius of the larger cone

Answer 16

is the volume .39 pi?..

Answer 17

yes good

Answer 18

now find the volume of the smaller cone

Answer 19

how do i find that?

Answer 20

the height is the same

Answer 21

but the radius is different

Answer 22

the radius of the smaller cone is...


Radius of smaller cone = (Radius of larger cone) - (Thickness of funnel)

Answer 23

.565

Answer 24

now use this to find the volume of the smaller cone

Answer 25

2.0114pi

Answer 26

that's not quite it

Answer 27

umm what did i do wrong?

Answer 28

you have r = 0.565 and h = 3.56 right?

Answer 29

yes

Answer 30

The volume of the smaller cone is...

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

\[\Large V = \frac{\pi*(0.565)^3*3.56}{3}\]

\[\Large V = \frac{\pi*0.180362125*3.56}{3}\]

\[\Large V = \frac{\pi*0.180362125*3.56}{3}\]

\[\Large V = \frac{\pi*0.642089165}{3}\]

\[\Large V = \pi*0.21402972166667\]

\[\Large V = 0.2140297\pi\]

which is approximate

Answer 31

hopefully you'll be able to spot your error

Answer 32

yesyes! I see

Answer 33

alright great

Answer 34

The volume of the funnel is then the difference between the two volumes

Answer 35

of the two cones

Answer 36

1.19 in3

1.78 in3

0.76 in3

3.57 in3

Answer 37

those are the answer options.....is it .76?

Answer 38

?????/

Answer 39

one sec

Answer 40

ok

Answer 41

just rechecking all that we did so far to make sure it's all correct

Answer 42

does that seem right tho

Answer 43

no I'm getting something much higher

Answer 44

what did you get?

Answer 45

oh wait...i made a silly typo...

Answer 46

the formula should be

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

I apologize

Answer 47

So the volume of the larger cone is

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

\[\Large V = \frac{\pi*(0.69)^2*3.56}{3}\]

\[\Large V = \frac{\pi*0.4761*3.56}{3}\]

\[\Large V = \frac{1.694916\pi}{3}\]

\[\Large V = 0.564972\pi\]

Answer 48

and the volume of the smaller cone is

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

\[\Large V = \frac{\pi*(0.565)^2*3.56}{3}\]

\[\Large V = \frac{\pi*0.319225*3.56}{3}\]

\[\Large V = \frac{1.136441\pi}{3}\]

\[\Large V = 0.378814\pi\]

Answer 49

so what's the answer?

Answer 50

Well I'm getting 0.58...so it can't be the difference...maybe they just want the volume of the smaller cone

So that would be...


\[\Large V = 0.378814\pi\]

\[\Large V = 0.378814(3.14159)\]

\[\Large V = 1.19007827\]

which is choice A

Answer 51

thank you sososo much! thanks for your time

Answer 52

you're welcome