ellie’s bird feeder is shaped like a cone with a height of 25 in. and a radius of 3 in. packages of bird seed are cylindrical and come in different sizes.
what is the height of the package that has a radius of 5 in. and contains exactly enough bird seed to fill the feeder? use 3.14 to approximate pi.
in.

jade scooped sand from a completely filled cylinder using a cone-shaped container. the cylinder had a diameter of 12 in. and a height of 5 in., and was one-fourth full after she scooped one full scoop of sand.
what were the dimensions of the cone-shaped container? use 3.14 to approximate pi.
a.
h = 5 in.; r = 9 in.
b.
h = 9.6 in.; r = 15 in.
c.
h = 11.25 in.; r = 12 in.
d.
h = 15 in.; r = 6 in.

 Ellie's bird feeder:

We're trying to find a cylinder that has exactly the same volume as a certain cone. The first thing we need is the formulas for the volumes of cones and cylinders.

               Volume of a cone = (1/3) (pi) (radius)² (height)

               Volume of a cylinder = (pi) (radius)² (height)

We know all the measurements of the cone. We also know the radius of the cylinder.  We want their volumes to be equal, and we need to find the height of the cylinder that will make them equal.

Here's the easiest way to do it:
Write an equation that says the volumes are equal.  In that equation, the height of the cylinder will be the only thing we don't know, and we can use the equation to find what it is.

                               Cone volume = Cylinder volume

  (1/3) (pi) (cone-R)² (cone-hight) = (pi) (cyl-R)² (Cyl-height)

Divide each side by (pi):

         (1/3) (cone-R)² (cone-hight) = (cyl-R)² (Cyl-height)

Put in all the numbers we do know:

                      (1/3) (  3  )²  (  25  ) = (  5  )² (Cyl-height)

                    (  1/3  x  9  ) x (  25  ) = (  25 ) x (Cylinder height)

Divide each side by 25:   (1/3 x 9) = Cylinder height.

                                      3 inches = Cylinder height


Jade scooping sand:

I'm sorry.  Maybe I don't understand the question, but I have to say
that none of the answers on the list is possible.

-- She has a cylinder that's completely full of sand, and she's using a
cone-shaped scooper to scoop sand out of the cylinder.

-- That means she has to slip the cone-shaped scooper down and
bury it in the sand, and then turn it right-side-up,and lift it out of the
cylinder along with the sand that's in it.

-- She can't get the scooper into the cylinder if the scooper's diameter
is bigger than the cylinder's diameter.  It won't fit.

-- The cylinder's diameter is 12 .  Its radius is 6.  The scooper's radius
can't be more than 6, or it won't fit.

In choices 'A', 'B', and 'C', the radius of the scooper is more than 6,
so none of those can even fit into the cylinder.

In choice 'D', the radius and diameter of the scooper is the same as
the cylinder, but its height (15) is three times the height of the cylinder !
I can't imagine how you could even scoop with it at all.

and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

.

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .

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