On a square handkerchief,nine circular designs each of radius 9cm are made. Find the area of the remaining portion of the handkercheif.
Assuming that the circles are arranged in a 3 by 3 pattern, and their continuous diameters are parallel to the sides of the square ....
the square would 54 cm by 54 cm, with an area of 2916 cm^2
the area of the circles is 9(π(81)) cm^2 = ...
take the difference between the two areas.
give clear answer
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To find the area of the remaining portion of the handkerchief, we need to subtract the total area occupied by the circular designs from the area of the square handkerchief.
Step 1: Find the area of each circular design.
The formula to find the area of a circle is A = πr^2, where A is the area and r is the radius. In this case, the radius is given as 9cm.
So, the area of each circular design is: A = π * (9cm)^2 = π * 81cm^2.
Step 2: Find the total area occupied by the circular designs.
Since there are nine circular designs, we multiply the area of one circular design by the number of designs: Total area = 9 * (π * 81cm^2).
Step 3: Find the area of the square handkerchief.
The square handkerchief has four equal sides, so we can say each side is equal to the radius of the circular designs, which is 9cm.
The formula to find the area of a square is A = side^2. In this case, the side length is 9cm.
So, the area of the square handkerchief is: A = (9cm)^2 = 81cm^2.
Step 4: Subtract the total area occupied by the circular designs from the area of the square handkerchief.
Remaining area = Area of the square handkerchief - Total area occupied by the circular designs.
Remaining area = 81cm^2 - (9 * π * 81cm^2) = 81cm^2 - 729πcm^2.
Therefore, the area of the remaining portion of the handkerchief is 81cm^2 - 729πcm^2.