A baker is decorating the top of a round cake with cherries. The diameter is 10 inches. Each cherry is 2 inches in diameter. About how many will the baker need to decorate the top of the cake?
A = pi * r^2
A = 3.14 * 25
A = 78.5 sq. in.
Divide the area by 2 to find the number of cherries.
Nummy!
The baker is filling the area of the cake with cherries.
Area=(pi)(r)(r)
so the big cake has a diameter of 10 inches. The radius is half of the diameter so r=5 inches
So the area of the top of the cake is
3.14159x5x5 = 78.53975
now you find the area of each cherry : )
Then take the total area of the cake and DIVIDE by the cherry area, and that will give you the number of cherries.
We will be happy to check your final answer : )
NUmmy!!
I don't think the problem is as simple as it appears.
By simply dividing the area of the cake by the area occupied by a cherry, does not allow
for the spaces left by adjoining cherries.
If we stack the cherries in rectangular patterns, then each cherry would occupy a
square area of 2by2 or 4 in^2
If they are stacked in a triangular pattern (like billiard balls in a rack), it gets even more complicated since the outer edge of the cake is circular.
Anyway, sounds like a delicious cake.
You don't stack the cherries. You lovingly lay them side by side, just on the top of the cake : )
I admit I used the wrong word in "stack", but the problem of the empty space between the cherries, which is included in the πr^2 calculation, still exists.
btw, my mother literally stacked the cherries, there were lots of them, all the more delicious.
Nummy!!
Now back to the problem at hand...
Notice in the wording it says "approximately" how many are needed.
I believe this is a gentle, get them excited about cherry topping on a cake, and not a "space between the cherries" needs to be considered problem.
But... what do I know?? I saw SUGAR CAKE... and all my good math sense went right out the window : )
To find out about how many cherries the baker will need to decorate the top of the cake, we need to calculate the number of cherries that can fit in the circular area.
First, we find the area of the circular cake. The formula for the area of a circle is A = πr², where A represents the area and r represents the radius of the circle. The diameter of the cake is given as 10 inches, so the radius is half of that, which is 10/2 = 5 inches.
Now we find the area of each cherry. Since the cherries are also round, we use the same formula A = πr², but this time the radius is 2/2 = 1 inch, as the diameter is given as 2 inches.
Next, we divide the area of the cake by the area of each cherry to find out how many cherries can fit. But first, let's calculate the areas:
Area of the cake = π(5 inches)² ≈ 78.54 square inches
Area of each cherry = π(1 inch)² ≈ 3.14 square inches
Now, divide the area of the cake by the area of each cherry:
Approximate number of cherries = Area of the cake / Area of each cherry
≈ 78.54 square inches / 3.14 square inches
≈ 25 cherries (rounded to the nearest whole number)
Therefore, the baker will need about 25 cherries to decorate the top of the round cake.