Final answer:
The shaded area of the semi-circle with a diameter of 24 mm is calculated by finding the area of the full circle and then halving it. After using the area formula A = πr² and inputting the radius of 12 mm, we find the semi-circle's shaded area to be 226 mm² when rounded to three significant figures.
Step-by-step explanation:
To calculate the shaded area, we need to understand that a circle fitting inside a semi-circle with a diameter of 24 mm has a radius of half that value, which is 12 mm. The area of a circle is calculated using the formula A = πr². Applying the radius of 12 mm, we get:
A = π×12² mm²
A = π×144 mm²
A ≈ 3.1415927×144 mm²
A ≈ 452.3893424 mm²
However, this includes the whole circle, but we only need the semi-circle area. So, we halve the area:
Shaded area ≈ 452.3893424 mm² / 2
Shaded area ≈ 226.1946712 mm²
Rounded to three significant figures, the shaded area is 226 mm².
The correct answer is c. 226 mm².