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A multi-layer cake is in the shape of a right cylinder. The height of the cake is 20 centimeters (cm), and its radius is 10cm. If each of the cake layers has a volume of approximately 1,250 cubic centimeters, then how many layers does the cake have? ◻

A multi-layer cake is in the shape of a right cylinder. The height of the cake is 20 cm20\,\text{cm}, and its radius is 10 cm10\,\text{cm}. If each of the cake layers has a volume of approximately 1,250 cubic centimeters1,250\,\text{cubic centimeters}, then how many layers does the cake have?\newline◻

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Full solution

Q. A multi-layer cake is in the shape of a right cylinder. The height of the cake is 20 cm20\,\text{cm}, and its radius is 10 cm10\,\text{cm}. If each of the cake layers has a volume of approximately 1,250 cubic centimeters1,250\,\text{cubic centimeters}, then how many layers does the cake have?\newline◻
  1. Calculate Cake Volume: Calculate the volume of the entire cake using the formula for the volume of a cylinder, which is V=πr2hV = \pi r^2 h, where rr is the radius and hh is the height.
  2. Determine Number of Layers: Determine the number of layers in the cake by dividing the total volume of the cake by the volume of one layer.
  3. Calculate Layers: Calculate the number of layers using the value of π\pi as approximately 3.141593.14159.
  4. Round to Whole Number: Since the number of layers must be a whole number, round the result to the nearest whole number.

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