The adjoining circle with centre o has radius of 14 cm .ABCD is a square drawn inside the circle calculate the area of the shaded region.
Where the f is answer
To calculate the area of the shaded region, we need to identify which parts of the circle are shaded and calculate their area.
In this case, we have a square (ABCD) inscribed inside the circle with center O. The shaded region refers to the area outside the square but inside the circle.
To calculate the area of the shaded region, we'll need to find the area of the circle and subtract the area of the square.
Step 1: Calculate the area of the circle
The area of a circle can be calculated using the formula A = πr^2, where A is the area and r is the radius.
In this case, the radius of the circle is given as 14 cm, so we can substitute this into the formula:
A_circle = π(14)^2
Step 2: Calculate the area of the square
The area of a square can be calculated by squaring the length of one of its sides.
Since the square is inscribed inside the circle, the diagonals of the square are equal to the diameter of the circle. Therefore, the diagonal of the square has a length of 14 cm.
Using the Pythagorean theorem, we can find the length of one side of the square:
(side)^2 + (side)^2 = (diagonal)^2
(side)^2 + (side)^2 = (14)^2
2(side)^2 = 196
(side)^2 = 98
side = √98
Now that we have the length of one side of the square, we can calculate its area:
A_square = (side)^2
Step 3: Calculate the area of the shaded region
Finally, we can calculate the area of the shaded region by subtracting the area of the square from the area of the circle:
A_shaded = A_circle - A_square
Note: Make sure to use the appropriate value of pi (π) for your calculations. The value of π can be approximated as 3.14159 or you can use a more accurate value if required.
Now, plug in the values and perform the calculations to find the area of the shaded region.
Yes
I am assuming you have a square centered within a circle of radius 14, and the "shaded region" in the region between circle and square.
draw a diagonal of the square, this will be the diameter of the circle and will be 28 cm long.
If the side of the square is x cm
x^2 + x^2 = 28^
2x^2 = 784
x^2 = 392
x = √392 or 14√2
the area of the circle is π(14^2) = 196π cm^2
the area of the square is 392 cm^2
so your shaded region .......