maths

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a cylindrical cake with radius 12cm and height 10cm has a slice cut out. The shape of the top of the slice is a sector of the circle that forms the top of the cake. Exluding the sliced piece, the angle is 320 degrees.
a) Calculate the area on top of the slice that has been cut out.
b) Calculate the volume of the cake that remains after the slice has been removed.
c) Calculate the surface area of the cake that remains after the slice has been removed.

i particularly need to know how to do c) This is bcause I have already worked out the answers to a) and b)

  • maths -

    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

  • maths -

    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

  • maths -

    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?

  • maths -

    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?

  • maths -

    no its leaving 40 degrees of the cake left, 320 is wot is there

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