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A baker uses a coffee mug with a diameter of 8cm to cut out circular cookies from a big sheet of cookie dough. What is the area A of each cookie? Give your answer in terms of pi. A=◻quad+x^(⇀)cm^(2)

A baker uses a coffee mug with a diameter of 8 cm 8 \mathrm{~cm} to cut out circular cookies from a big sheet of cookie dough.\newlineWhat is the area A A of each cookie? Give your answer in terms of pi.\newlineA=□ A=\square  cm2\mathrm{~cm}^{2}

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Full solution

Q. A baker uses a coffee mug with a diameter of 8 cm 8 \mathrm{~cm} to cut out circular cookies from a big sheet of cookie dough.\newlineWhat is the area A A of each cookie? Give your answer in terms of pi.\newlineA=□ A=\square  cm2\mathrm{~cm}^{2}
  1. Find Radius of Cookies: First, we need to find the radius of the cookies since the area of a circle is calculated using the radius. The radius is half of the diameter.\newlineRadius = Diameter / 22 = 8 cm/2=4 cm8\,\text{cm} / 2 = 4\,\text{cm}.
  2. Calculate Area of Circle: Now, we can use the formula for the area of a circle, which is A=π∗r2A = \pi * r^2, where rr is the radius.\newlineA=π∗(4 cm)2A = \pi * (4\,\text{cm})^2.
  3. Square Radius: Squaring the radius gives us 16 cm216\,\text{cm}^2. \newlineA = π×16 cm2\pi \times 16\,\text{cm}^2.
  4. Final Area Calculation: So, the area of each cookie is 16π cm216\pi \, \text{cm}^2.

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