maths

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 because I have already worked out the answers to a) and b)

c)
I worked out the area 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?

  1. 👍
  2. 👎
  3. 👁
  1. It's me again.

    I now fully understand what you are asking for in your part c)

    I agree with your calculations of the exposed area of the top and bottom of the remaining cake
    area (top+bottom) = 2(320/360)(144π) = 804.25 (you had that)

    area (exposed outer side) = (320/360)(2π(12))(10) = 670.21 (you had that also)

    if we add just those two sums we get 1474.45 which is their answer.
    So it does look like they forgot the 2 rectangular areas of the inside of the remaining cake, which you calculated correctly as well, which were 2(12)(10) = 240

    so the correct answer should have been the sum of those 3 answers or 1714.45 which you also had.

    I again apologize for my error in our last exchange.

    1. 👍
    2. 👎
  2. thankyou, I wanted to know whether I was right or the textbook because it was very rare that they make mistakes, I wanted to clarify whether it makes sense to add the 2 sides area=240. I thought it did so Im going to leave it how I did it.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    Find the diameter and the height of a cylinder of maximum volume which can cut from a sphere of radius 12cm

  2. calculus

    A candy company needs a custom box for their truffles. The box they've chose is in the shape of a cylinder with a hemisphere of the same radius on top. The total volume of the box is V= (1/2) ((4pir^2)/(3))+ pir^2 (y-r), where y

  3. calculus

    A rectangular beam is cut from a cylindrical log of radius 25 cm. The strength of a beam of width w and height h is proportional to wh2. (See Figure 4.70.) Find the width and height of the beam of maximum strength.

  4. Calculus

    A wire 60 cm long is to be cut into two pieces. One of the pieces will be bent into the shape of a square and the other into the shape of an equilateral triangle, as shown in the diagram below: a diagram showing a 60 cm wire cut

  1. Math

    A copper solid cylinder of radius 14cm and height 10cm is melted and recast into cylindrical wire of diameter 4mm.find the length of the copper wire

  2. algebra

    The volumes of two cylindrical cans of the same shape vary directly as the cubes of their radii. If a can with a six-inch radius holds 1½ pints, how many gallons will a similar can with a 24-inch radius hold?

  3. calculus inverted cone

    A container in the shape of an inverted cone has radius 6 ft and height 12 ft. It is being drained at 2〖ft〗^3/min. Find the rate of change of the height of the liquid in the cone when the height is 3 feet. The ratio of the

  4. Maths

    If a marble of radius 2.1 cm is put into a cylindrical cup of radius 6cm and height 8cm, then how much water flows out of it.?

  1. math

    taylor baked a cake to serve after dinner. suppose she cut the cake into 8 equal size pieces and 6 people ate all the pieces. explain how they could have didided the pieces so that everyone ate the same amount of cake. you may

  2. bugema university

    . A container in the shape of a right circular cone of height 10cm and base radius 1cm is catching water from a tap leaking at the rate of 0.1cm3 s -1 . Find the rate at which the surface area of water is increasing when the water

  3. Maths

    A wire is in the shape of a square of side 10cm. If the wire is rebent in to a rectangle of length 12cm.find its breadth which figure encloses more area and by how much.

  4. maths

    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

You can view more similar questions or ask a new question.