Difference between revisions of "2021 WSMO Accuracy Round Problems/Problem 6"
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| + | ==Problem== | ||
| + | Roy is baking a circular three tier cake. All of the tiers are centered around the same point. Each tier's radius is <math>\frac{3}{4}</math> of the radius of the tier below it, but the height of each tier stays constant. Roy wants to ice the cake, but only on the curved surfaces of the cake and the top of the smallest tier. The diameter of the lowest tier is <math>128</math> centimeters and its height is <math>10</math> centimeters. If the surface area that is iced can be expressed as <math>m\pi,</math> find <math>m.</math> | ||
| + | ==Solution 1== | ||
So there is a 3 tier cake i.e. 3 cylinders of the same height but different radii stacked over each other. | So there is a 3 tier cake i.e. 3 cylinders of the same height but different radii stacked over each other. | ||
The LOWERMOST Tier: Given Diameter = 128 => Radius = 64 and Height = 10 | The LOWERMOST Tier: Given Diameter = 128 => Radius = 64 and Height = 10 | ||
Revision as of 09:02, 11 July 2022
Problem
Roy is baking a circular three tier cake. All of the tiers are centered around the same point. Each tier's radius is 
of the radius of the tier below it, but the height of each tier stays constant. Roy wants to ice the cake, but only on the curved surfaces of the cake and the top of the smallest tier. The diameter of the lowest tier is 
centimeters and its height is 
centimeters. If the surface area that is iced can be expressed as 
find 
Solution 1
So there is a 3 tier cake i.e. 3 cylinders of the same height but different radii stacked over each other. The LOWERMOST Tier: Given Diameter = 128 => Radius = 64 and Height = 10 So Surface Area Iced = 2πrh = 2*π*64*10 = 1280π
The MIDDLE Tier : Radius = 3/4*64 = 48 and Height = 10 So Surface Area Iced = 2πrh=2*π*48*10 = 960π
The TOPMOST Tier : Radius = 3/4*48 = 36 and Height = 10 So Surface Area Iced = 2πrh=2*π*36*10 = 720π
The Top Layer of TOPMOST Tier : Radius = 36 So Surface Area Iced = πr^2 = π*36*36 = 2592π
Thus Total Surface Area Iced = 1280π+960π+720π+2592π = 5552π
SO m=5552
~AshutoshVerma
