Question

5. Sarah and Aarnav had a 3-layer wedding cake made for their wedding. Each layer was 6 inches in height. The lower layer had a diameter of 12 inches, while the middle layer had a radius of 5 inches. The top layer had a diameter of 8 inches.

a) Calculate the total volume of cake to the nearest cubic inch. (3 marks)











b) The baker who made the cake needed to calculate the total surface area of the outside of the cake to the nearest square inch to find out how much icing to buy. The baker will not be icing the bottom of any of the layers of cake. However, the baker will ice the top and sides of each layer separately and then stack the three layers of cake. Calculate the surface area of the cake that the baker plans to ice to the nearest square inch. (3 marks)












c) The baker bought the buttercream icing from Crave Cupcakes. Using your surface area calculation from part b, calculate how many containers of icing the baker needs to buy in order to ice Sarah and Aarnav’s cake. Each container of icing contains 16 ounces of icing. If it takes 56 ounces of icing to cover 678 square inches of cake, calculate the total cost for the icing before tax if each 16-ounce (2 cup) container of icing costs $10. (3 marks)

Answer 1

Total volume of cake = 1452 cubic inches

Explanation:

Each layer of the cake has a cylindrical shape, so that:

volume of a cylinder =
`\pi`
`r^(2)`h

Where r is the radius and h represents the height.

i. For the lower layer;

h = 6 inches and r = 6 inches

volume =
`\pi`
`r^(2)`h

=
`(22)/(7)` x
`(6)^(2)` x 6

= 678.86 cubic inches

ii. For the middle layer;

h = 6 inches and r = 5 inches

volume =
`\pi`
`r^(2)`h

=
`(22)/(7)`x
`(5)^(2)` x 6

= 471.43 cubic inches

iii. For the top layer;

h = 6 inches and r = 4 inches

volume =
`\pi`
`r^(2)`h

=
`(22)/(7)` x
`(4)^(2)`x 6

= 301.71 cubic inches

Total volume of cake = 678.86 + 471.43 + 301.71

= 1452 cubic inches