Verified answer

Problem:

Today is Joseph's wedding. He went to the bakeshop to pick-up his wedding cake. He instructed the baker that the cross-section area of each of the two bottom layers of the wedding cake is double to cross section area of the layer on top and the three layers have the same height.

Asked:

What is the volume of the cake?

Solution:

Information to keep in mind

• r₁ = 20cm (bottom layer)
• r₂ = 20/10 = 10cm (middle layer)
• r₃ = 10/2 = 5cm (top layer)
• h (of each layer) = 15cm

Formula of a cylinder

• V = πr²h

Volume (total)

• V = πr₁²h + πr₂²h + πr₃²h
• V = πh (r₁² + r₂² + r₃²)
• V = 3.14 x 15 ([20]² + [10]² + [5]²)
• V = 47.1 (400 + 100 + 25)
• V = 47.1 (525)
• V = 24,727.5 cm³

Answer:

Therefore, The volume of the cake is 24,727.5 cm³.

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