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?

Identify Formula and Values: Identify the formula for the volume of a cylinder and the given values. Volume of a cylinder = π * radius^2 * height Given: radius = 10 cm, height of each layer = unknown, volume of each layer = 1,250 cm³Calculate Cake Volume: Calculate the volume of the entire cake using the formula for the volume of a cylinder. Volume of the entire cake = π * (10 cm)^2 * 20 cm Volume of the entire cake = π * 100 cm² * 20 cm Volume of the entire cake = 2000π cm³Find Number of Layers: Divide the total volume of the cake by the volume of one layer to find the number of layers. Number of layers = Total volume of the cake / Volume of one layer Number of layers = 2000π cm³ / 1,250 cm³Perform Division: Perform the division to find the number of layers. Number of layers ≈ 2000π / 1,250 Number of layers ≈ 8π Since π is approximately 3.14159, we can approximate the number of layers. Number of layers ≈ 8 * 3.14159 Number of layers ≈ 25.13272Round to Nearest Whole Number: Since the number of layers must be a whole number, round the result to the nearest whole number. Number of layers ≈ 25

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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 $20$ centimeters $(\mathrm{cm})$ , and its radius is $10 \mathrm{~cm}$ . If each of the cake layers has a volume of approximately $1$ , $250$ cubic centimeters, then how many layers does the cake have?

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Q. A multi-layer cake is in the shape of a right cylinder. The height of the cake is

20

centimeters

(\mathrm{cm})

, and its radius is

10 \mathrm{~cm}

. If each of the cake layers has a volume of approximately

1

250

cubic centimeters, then how many layers does the cake have?

Identify Formula and Values: Identify the formula for the volume of a cylinder and the given values. $\newline$ Volume of a cylinder = $\pi \times \text{radius}^2 \times \text{height}$ $\newline$ Given: radius = $10\,\text{cm}$ , height of each layer = $20\,\text{cm}$ , volume of each layer = $1,250\,\text{cm}^3$
Calculate Cake Volume: Calculate the volume of the entire cake using the formula for the volume of a cylinder. $\newline$ Volume of the entire cake = $\pi \times (10 \, \text{cm})^2 \times 20 \, \text{cm}$ $\newline$ Volume of the entire cake = $\pi \times 100 \, \text{cm}^2 \times 20 \, \text{cm}$ $\newline$ Volume of the entire cake = $2000\pi \, \text{cm}^3$
Find Number of Layers: Divide the total volume of the cake by the volume of one layer to find the number of layers. $\newline$ Number of layers $= \frac{\text{Total volume of the cake}}{\text{Volume of one layer}}$ $\newline$ Number of layers $= \frac{2000 \pi \, \text{cm}^3}{1,250 \, \text{cm}^3}$
Perform Division: Perform the division to find the number of layers. $\newline$ Number of layers $\approx \frac{2000\pi}{1,250}$ $\newline$ Number of layers $\approx 1.6\pi$ $\newline$ Since $\pi$ is approximately $3.14159$ , we can approximate the number of layers. $\newline$ Number of layers $\approx 1.6 \times 3.14159$ $\newline$ Number of layers $\approx 5.026544$
Round to Nearest Whole Number: Since the number of layers must be a whole number, round the result to the nearest whole number. $\newline$ Number of layers $\approx 5$