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

We use the area formula for a circle, which is  
$$
A = \pi r^2,
$$  
where $$ r $$ is the radius (half the diameter).

1. For the $$ 8 $$-inch cake:  
   - Radius: $$ r = \frac{8}{2} = 4 $$ inches  
   - Area:  
     $$
     A_1 = \pi (4)^2 = 16\pi \approx 50.3 \text{ in}^2
     $$

2. For the $$ 12 $$-inch cake:  
   - Radius: $$ r = \frac{12}{2} = 6 $$ inches  
   - Area:  
     $$
     A_2 = \pi (6)^2 = 36\pi \approx 113.1 \text{ in}^2
     $$

3. For the $$ 15 $$-inch cake:  
   - Radius: $$ r = \frac{15}{2} = 7.5 $$ inches  
   - Area:  
     $$
     A_3 = \pi (7.5)^2 = 56.25\pi \approx 176.7 \text{ in}^2
     $$

Thus, the correct areas are  
$$
A_{1}=50.3 \text{ in}^{2}; \quad A_{2}=113.1 \text{ in}^{2}; \quad A_{3}=176.7 \text{ in}^{2}.
$$
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.