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
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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.
