Find the total area of the shaded region sho The total area of the shaded region is Ok
The Correct Answer and Explanation is:
The correct answer is 50π cm².
To find the total area of the shaded region, we must first calculate the area of the large outer circle and then subtract the combined area of the two smaller, unshaded circles within it.
First, let’s determine the area of the large circle. The problem states that the radius of the large circle is 10 cm. The formula for the area of a circle is A = πr², where ‘r’ is the radius. By substituting the given radius into this formula, we find the area of the large circle is π multiplied by (10 cm)², which equals 100π cm².
Next, we need to find the area of the two smaller circles. From the image, we can see that the diameters of the two identical smaller circles lie along the diameter of the large circle. The diameter of the large circle is twice its radius, so it is 2 * 10 cm = 20 cm. Since the two small circles span this length, the diameter of each small circle must be half of the large circle’s diameter, which is 20 cm / 2 = 10 cm. Therefore, the radius of each small circle is half of its diameter, or 10 cm / 2 = 5 cm.
Now we can calculate the area of one small circle using the same area formula, A = πr². With a radius of 5 cm, the area of one small circle is π multiplied by (5 cm)², which results in 25π cm². Since there are two identical unshaded circles, their total area is 2 * 25π cm², which is 50π cm².
Finally, to find the area of the shaded region, we subtract the total area of the two small circles from the area of the large circle. This calculation is 100π cm² – 50π cm².
The resulting total area for the shaded region is 50π cm².