Our first instinct is to go through every step ...
-- calculate the volume of the bowl
-- calculate the volume of the ladle
-- divide the volume of the bowl by the volume of the ladle
and we may even start down that path. But we soon realize that
it's going to be painful and take a lot of time. So we stop right
where we are, and consider our options.
We have two options:
#1). Give up, quit, and walk away.
#2). Find a smarter way to do it.
Look at the formula for the volume of a sphere:
Volume = (4/3 π) (radius³) .
Do you see that ? The radius³ is a factor in the volume of
every sphere. That means that if you multiply the radius
of a sphere by (a number), the volume of the sphere gets
multiplied by (the same number)³ !
How does that help us with this problem ? Well, it also means
that the ratio of the volumes of two spheres is
(the ratio of their radii)³.
Radius of the bowl = 15 inches
Radius of the ladle = 4 inches
Ratio of their radii = (15/4) = 3.75
So the bowl holds (3.75)³ as much as the ladle holds.
(3.75)³ = 52.73 ...
The bowl holds 52.73 ... times as much as the ladle.
After Grandma Edith scoops 52 ladle-fulls from the bowl,
there will be less than 1 ladle-full remaining in there.
And we did it all without even knowing π .