Question

The volume of a cone that fits exactly inside a cylinder is 20 cubic feet. What is the volume of the cylinder?

Answer 1

@whpalmer4

Answer 2

If a cone fits exactly inside a cylinder (both have the same radius and height), then the rule is this


Volume of Cylinder = 3*(Volume of Cone)

Answer 3

x=3*20?

Answer 4

Basically this is saying that you can fit 3 of these cones in the cylinder.

Answer 5

exactly, so 60 cubic feet

Answer 6

can you help me with another one?

Answer 7

sure

Answer 8

Using the following equation, find the center and radius:

x2 − 4x + y2 + 8y = −4

Answer 9

i know that you have to isolate them

Answer 10

no you just need to get it into the form (x-h)^2 + (y-k)^2 = r^2

Answer 11

you do that by completing the square for x and y

Answer 12

i dont get it

Answer 13

what is the x coefficient?

Answer 14

2 and -4

Answer 15

2 is the exponent

Answer 16

-4 is the coefficient for the x term

Answer 17

cut that in half to get what?

Answer 18

-2

Answer 19

square that to get ???

Answer 20

4

Answer 21

now add that to both sides

Answer 22

Doing that gives you

x^2 - 4x + y^2 + 8y = -4

x^2 - 4x + y^2 + 8y + 4 = -4+4

x^2 - 4x + y^2 + 8y + 4 = 0

Answer 23

now if you rearrange terms, you would get this

x^2 - 4x + y^2 + 8y + 4 = 0

(x^2 - 4x + 4) + y^2 + 8y = 0

what do you get when you factor x^2 - 4x + 4 ?

Answer 24

(x−2)^2

Answer 25

good

Answer 26

we now have

(x-2)^2 + y^2 + 8y = 0

Answer 27

so we're halfway done

Answer 28

do the same thing for the y terms

find the y coefficient, take half of that, then square that to get ???

Answer 29

coefficients : 1,8

Answer 30

not the y^2 term, just the y term

Answer 31

sorry I should have clarified

Answer 32

but i dont know how to take half

Answer 33

what is the y coefficient? of the y term, not the y^2 term

Answer 34

8

Answer 35

cut that in half, then square that result

Answer 36

16

Answer 37

add that to both sides

Answer 38

you'll have y^2 + 8y + 16 which factors to what?

Answer 39

(y+4)^2

Answer 40

good

Answer 41

we now have (x-2)^2 + (y+4)^2 = 16

Answer 42

what is the center and radius?

Answer 43

Radius: 16
Center: (-2,4)

Answer 44

no

Answer 45

keep in mind that the center of (x-h)^2 + (y-k)^2 = r^2 is (h,k)

the radius of (x-h)^2 + (y-k)^2 = r^2 is r

Answer 46

Center: (−2, −4)
Radius: 16.

Answer 47

Is that right?

Answer 48

@jim_thompson5910 you there?

Answer 49

(x-2)^2 + (y+4)^2 = 16

turns into

(x-2)^2 + (y - (-4))^2 = 4^2

Answer 50

notice how I'm replacing y + 4 with y - (-4). Think of this as two negatives canceling to make a positive

Answer 51

and I'm rewriting 16 as 4^2

Answer 52

now list off: h, k, r

Answer 53

use (x-h)^2 + (y-k)^2 = r^2 as a template

Answer 54

so what i put is not right?

Answer 55

no

Answer 56

the radius is 4?