To find the cost of the icing needed to decorate the cake, we first need to find the surface area of each tier of the cake and then sum them up.
For the first tier with a radius of 22 cm and height of 10 cm:
Surface area = 2πrh + 2πr^2
= 2π(22)(10) + 2π(22)^2
= 440π + 968π
= 1408π cm^2
For the second tier with a radius of 17 cm and height of 10 cm:
Surface area = 2πrh + 2πr^2
= 2π(17)(10) + 2π(17)^2
= 340π + 578π
= 918π cm^2
For the third tier with a radius of 12 cm and height of 10 cm:
Surface area = 2πrh + 2πr^2
= 2π(12)(10) + 2π(12)^2
= 240π + 288π
= 528π cm^2
Now, sum up the surface areas of all three tiers:
1408π + 918π + 528π = 2854π cm^2
The cost of icing per square centimetre is 2 cents. Therefore, the total cost to decorate the entire cake (except for its base) is:
2854π * 0.02 = $57.08
A wedding cake has three tiers. Each tier is 10cm high. The layers have radii 22 cm, 17 cm, and 12 cm respectively. The pastry chef needs to determine the cost of the icing needed to decorate the cake. If icing costs 2 cents per square centimetre, how much will it cost to decorate the entire cake (except for its base)?
1 answer