Question 1

The area of the circle is 31.79 cm squared.

To find the area of a circle, the formula \( A = \pi r^2 \) is used. With a radius of 4.5 cm, the area calculates to approximately 31.79 cm squared.

A) 28.26 cm squared

This option is incorrect because the area calculated using the formula does not yield this result. Specifically, when applying the radius of 4.5 cm in the formula \( A = \pi (4.5)^2 \), the outcome is significantly different from 28.26 cm squared.

B) 31.79 cm squared

This option is correct. By substituting the radius of 4.5 cm into the area formula \( A = \pi (4.5)^2 \), the calculation results in approximately 31.79 cm squared, confirming this as the accurate area of the circle.

C) 15.90 cm squared

This choice is incorrect as it represents a miscalculation of the area. The area formula clearly shows that the correct area must be larger, as \( 4.5^2 \) multiplied by \( \pi \) does not yield 15.90 cm squared.

D) 63.59 cm squared

This option is also incorrect. While it might seem plausible if one incorrectly used the radius or misapplied the formula, the actual area calculation with the given radius leads to a much smaller value than 63.59 cm squared.

Conclusion

The correct answer, 31.79 cm squared, is derived directly from applying the formula for the area of a circle using the radius provided. All other options either result from incorrect calculations or misunderstandings of the formula, highlighting that option B is the only viable answer based on the given information.