Posted by Anonymous on Thursday, April 22, 2010 at 5:35pm.
ahhh, I knew you left something out
So the slice cut out has a 60° central angle, so its surface area must be 1/6 of the whole circle surface area, or (1/6)π(144)
and the part remaining must be (5/6)(144)π = 120π
why is it a 60 degrees central angle? arent you supposed to break the cylindrical cake into parts: top and bottom, 2 rectangles where the slice has been cut inside, outside curved when opened out becomes long rectangle?? then work out the area of each part then add up. i want to know how you calculate the area of each of those parts.I know how to do a rectangle
I see it as a simple round cake where we cut out a slice (a sector) leaving 320° of cake left.
I have no idea where you are getting your interpretation. Since when are cakes cut into tops and bottoms?
You say you got a) and b)
Were there answers given to this question?
not tops and bottoms, i mean like you have to work out the area of the top of the cake using the sector 320 degrees, but there is also a bottom so you therefore have to multiple it by 2.
same with when you cut the slice- there are 2 rectangular sides. obviously round the circumference of the cake there is a long rectangular shape but because it is a cake it looks curved. because you want the whole surface area once you've sliced it you have to add all the figures. Here are my workings:
10*12=120*2=240cm squared
area of base=320 over 360*pie*12 squared=402.1238597*2 cos theres a top and bottom 4 a cake= 804.2477193
w=320 over 360*2*pie*12 ( multiply this by height of 10cm= 670.2064328
add these: 240+804.2477193+670.2064328=1714.454852 so surface area = 1414cm squared
however in the book the answer was 1474cm squared. i figured out they didn't add the 240 on which are the bits on the side- which is right?
no its leaving 40 degrees of the cake left, 320 is wot is there