Question

Geometry – show all work and a complete solution to earn the points. this is due on or before 11/9/23. each of the white circles has a radius of 1. each white circle is tangent to each other and to the circumference of the black circle. find the area of the shaded region. round your answers to the nearest 100th .

Answer 1

To find the area of the shaded region, calculate the area of the black circle and subtract the combined areas of the white circles. Use the formula A = πr^2 for the area of a circle.

Step-by-step explanation:

To find the area of the shaded region, we need to calculate the area of the black circle and subtract the combined areas of the white circles. Let's start by finding the area of the black circle. The formula for the area of a circle is A = πr2. Since the radius of the black circle is unknown, let's call it 'R'. So the area of the black circle is Ablack = πR2.

Now let's find the combined area of the white circles. Each white circle has a radius of 1, so the area of each white circle is Awhite = π(1)2 = π.

Since there are four white circles, the combined area of the white circles is Awhite_combined = 4π.

Finally, we can find the area of the shaded region by subtracting the combined area of the white circles from the area of the black circle: Ashaded = Ablack - Awhite_combined = πR2 - 4π.

To round the answer to the nearest hundredth, we can plug in the value of 'R' and use a calculator to calculate the final result.