A Venn diagram with two circles is drawn. Each circle has a diameter of 10 cm. The overlapping area is 20 cm^2. Find the total writing area within the diagram.
A = pi * r^2
A = 3.14 * 5^2
A = 78.5
(2 * 78.5) - 20 = ?
To find the total writing area within the diagram, we need to determine the combined area of the two circles and subtract the overlapping area.
Step 1: Find the area of one circle
Given that the diameter of each circle is 10 cm, the radius (r) would be half of the diameter, which is 10 cm / 2 = 5 cm.
Using the formula for the area of a circle (A = πr^2), we can calculate the area of one circle: A = π(5 cm)^2 = 25π cm^2.
Step 2: Find the combined area of both circles
Since there are two circles, we multiply the area of one circle by 2: 2 * 25π cm^2 = 50π cm^2.
Step 3: Subtract the overlapping area
Given that the overlapping area is 20 cm^2, we subtract it from the combined area of the circles: 50π cm^2 - 20 cm^2 = 30π cm^2.
So, the total writing area within the diagram is 30π cm^2 (or approximately 94.25 cm^2).