A cake shop offers circular cakes with diameters of $$ 8 \mathrm{in} ., 12 $$ in., and 15 in . Identify the area of each cake rounded to the nearest tenth. $$ A_{1}=201.1 \mathrm{in}^{2} ; A_{2}=452.4 \mathrm{in}^{2} ; A_{3}=706.9 \mathrm{in}^{2} $$ $$ A_{1}=50.3 \mathrm{in}^{2} ; A_{2}=113.1 \mathrm{in}^{2} ; A_{3}=176.7 \mathrm{in}^{2} $$ $$ A_{1}=12.6 \mathrm{in}^{2} ; A_{2}=18.8 \mathrm{in}^{2} ; A_{3}=23.6 \mathrm{in}^{2} $$ $$ A_{1}=25.1 \mathrm{in}^{2} ; A_{2}=37.7 \mathrm{in}^{2} ; A_{3}=47.1 \mathrm{in}^{2} $$

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UpStudy AI · Accepted Answer

The formula for the area of a circle is  
$$
A=\pi r^2
$$

1. For the 8-inch cake, the radius is  
$$
r=\frac{8}{2}=4 \text{ in}
$$  
Therefore, the area is  
$$
A_1=\pi \cdot 4^2=16\pi \approx 50.3 \text{ in}^2
$$

2. For the 12-inch cake, the radius is  
$$
r=\frac{12}{2}=6 \text{ in}
$$  
Thus, the area is  
$$
A_2=\pi \cdot 6^2=36\pi \approx 113.1 \text{ in}^2
$$

3. For the 15-inch cake, the radius is  
$$
r=\frac{15}{2}=7.5 \text{ in}
$$  
The area is then  
$$
A_3=\pi \cdot (7.5)^2=\pi \cdot 56.25 \approx 176.7 \text{ in}^2
$$

The correct set of areas rounded to the nearest tenth is:  
$$
A_{1}=50.3 \text{ in}^2; \quad A_{2}=113.1 \text{ in}^2; \quad A_{3}=176.7 \text{ in}^2
$$
The areas of the cakes are: - 8-inch cake: 50.3 in² - 12-inch cake: 113.1 in² - 15-inch cake: 176.7 in²

A cake shop offers circular cakes with diameters of
in., and 15 in . Identify the area of each cake rounded to the
nearest tenth.

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A cake shop offers circular cakes with diameters of in., and 15 in . Identify the area of each cake rounded to the nearest tenth.