Now regarding the shaded region. It definitely looks like a semicircle with PQ as the base. If PQ were a diameter, then O would be the midpoint of PQ. But O is the center of the circle, and PQ is a chord. The shaded region in the figure seems to be the area of the semicircle. Let's assume the shaded region is the semicircle whose diameter is the line segment from P to a point directly opposite on the circumference, passing through O. The shading is from P to Q, then along arc Q to another.
(semicircle, diameter, chord, circumference, arc)
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Step-by-Step Solution
Step 1: Identify the shape and given information
The problem states that the shaded region is a semicircle and that PQ is its diameter. We are given the length of the diameter, PQ=10 cm.
Step 2: Calculate the radius
The radius (r) of a circle or semicircle is half of its diameter (d). By dividing the given diameter by 2, we find the radius.
Step 3: Recall the formula for the area of a semicircle
The area of a full circle is given by the formula πr2. Since a semicircle is half of a circle, its area is half of the full circle's area.
Step 4: Substitute the radius and calculate the area
Now, we substitute the calculated radius r=5 cm into the area formula. We square the radius and then multiply by 21π to get the final area.