Question

You have a cake that is 10 inches in diameter. You expect 12 people to share it, so you cut it into 12 equal slices. Before you get a chance to serve the cake, 12 more people arrive! So, you decide to cut a concentric circle in the cake so that you will have 24 pieces. How far from the center of the cake should the circle cut be made so that all 24 people get the same amount of cake?

Answer 1

3.5355 inches

Explanation:

Area should be same the concentric circle and rest piece .

let's consider the radius of concentric circle as r

so it's area is π r²

area of whole circle is π (5)" ( because diameter is 10 inches)

so the area of rest piece is π (5)² - π r²

π (5)² - π r² = π r²

5² = 2r²

r² = 25/2

r = √(25/2)

r = 3.5355 inches