Question

A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of π.)

Answer 1

Do you know how to find the volume of the cylinder? How about the cone?

Answer 2

No im not good at geometry @whpalmer4

Answer 3

Well, do you have a textbook? Class notes? I'm sure you've been given the formulas, and aren't expected to derive them on your own!

Answer 4

I have these formulas

Answer 5

The first step in the problem is to make sure you have all the needed tools. Two of those tools are the equation for the volume of a cylinder and the equation for the volume of a cone.

Answer 6

Okay! So, what is the height of the cylinder, and what is its radius? We'll call those \(h\) and \(r\) respectively. Read the problem, and respond with something like
h=5 cm
r=2 cm
(except use the correct values, please!)

Answer 7

h=16 r=5
h=12 r=4

Answer 8

Good, you anticipated my next request :-)

Let's find the volume of that cylinder. As my capable assistant stated, h = 16 and r = 5.
The formula is \[V = \pi r^2 h\]Plug in the numbers and tell me what you get, though you should keep it in "symbolic" form: \(37\pi\) instead of \(116.239\), for example.

Answer 9

so V=Pi 5^2 (16)=400Pi ?

Answer 10

Very good! Now can you do the same for the cone, using r=4 and h = 12. The formula there is \[V=\frac{1}{3}\pi r^2h\]

Answer 11

=64Pi=201.06

Answer 12

Okay, if the volume of the cylinder is \(400\pi\) and the volume of the cone is \(64\pi\), how much space is left for air?

Answer 13

1457.698991?

Answer 14

Better to keep it in symbolic form while we figure out if you have the right expression or not. Then we don't have to worry about whether a difference in answers is because you had the wrong expression, or just didn't operate the calculator successfully.

Answer 15

336Pi?

Answer 16

Yes. What do you get when you convert that to a numeric form?

Answer 17

1055.04

Answer 18

That what I get, too.

Answer 19

would this be B?

Answer 20

Well, let's figure it out: we know the height is S, and we know the diameter is S. That means the radius is S/2. The volume of the cylinder is \[V = \pi r^2h = \pi (\frac{S}{2})^2S = \]

Answer 21

so the volume could = v=PiS^2?

Answer 22

No...

\[\V = \pi(\frac{S}{2})^2*S = \pi*(\frac{S*S}{2*2})*S = \]

Answer 23

v=1/4PiS^3?

Answer 24

There you go!

Answer 25

im thinking in terms of c.. a=2c/Pi

Answer 26

\[C = 2\pi r\]\[r = \frac{C}{2\pi}\]right?

then plug that into the formula for the area of a circle: \[A = \pi r^2\]

Answer 27

ok so it would be c^2/4Pi?

Answer 28

if by that you mean \[A = \frac{C^2}{4\pi}\]then yes.

Answer 29

this is the last one i promise

Answer 30

i got 12 cm^3 is that correct?

Answer 31

What's the formula for the volume of a pyramid?

Answer 32

\[V = \frac{1}{3}A_{base}h\]where \(A_{base}\) is the area of the base. What's the area of the base of this pyramid?