You now have 6 different posts going for the same "cake question"
I am not going to keep going back to see which one you replied to. Stay with one posting please.
I just notice one way down the list where you did part a) Calculate the area on top of the slice that has been cut out and you got 50.3 something
area = (60/360)(144π) = 24π = 75.4
ok sorry, but i don't get how you are getting that? where is the 60 and 144 coming from, my answers for both a and b were right- its just c
have you looked at my long explanation to see how I attempted it?
Ok,
You said after a slice is cut, there are 320° of cake left, so the slice must have had a sector angle of 60° , since there are 360° in one rotation.
Area of the whole top is πr^2 = π(12^2) = 144π
If you were trying to do it by ratios, then
area/144π = 60/360
area/144π = 1/6
area = (1/6)144π = 24π like I had
b) the volume of the whole cake = (πr^2)h
so again, a slice is 1/6 of that volume.
Nabiha, I just realized I made a very silly error.
Of course then angle of the slice is 40° and not 60
I am sorry to have caused you all this trouble.
so your answer to a) would be
(40/360)(144π) = 50.3, which I believe you had
change all my other calculations using the 1/6 to 1/9
because 40/360 = 1/9
ok, but what about question c) what formulas would I use, is my method correct?
that is by using sections and work out the area of the 3 parts: 1)rectangle * 2(shown by the slice being cut), 2)long rectangle around cake (stops when you get to slice) and finally 3)the top and bottom of the cake ( angle is 320)
how do I work out the area of 2) and 3) so then I can add them to get the total surface area with the slice cut
Ive already shown this in my long explanation of my method to c) can you please comment on that one aswell.
Apologies for the confusion with multiple posts. Let's focus on the question at hand.
To calculate the area on top of the slice that has been cut out, we need to find the measure of the angle of that slice.
In the given question, it states that a slice is cut from a circular cake with a radius of 10 inches. The slice has a central angle of 60 degrees.
To calculate the area of the slice, we can use the formula for the area of a sector of a circle, which is given by:
Area = (θ/360) * π * r^2
Where:
- θ is the central angle of the sector in degrees
- π represents the mathematical constant pi (approximately 3.14159)
- r is the radius of the circle
Plugging in the values from the question, we have:
Area = (60/360) * π * (10^2)
= (1/6) * π * 100
≈ 16.67 * 3.14159
≈ 52.35 square inches (rounded to two decimal places)
Therefore, the area on top of the slice that has been cut out is approximately 52.35 square inches.