Question 30

The area of the largest circle that can fit entirely inside the rectangle is 16π cm².

The largest circle that can fit inside a rectangle is determined by the smaller dimension of the rectangle, which dictates the diameter of the circle. In this case, the rectangle measures 8 cm by 10 cm, making the diameter of the circle 8 cm. Thus, the radius is 4 cm, leading to an area of 16π cm² for the circle.

A) 18π cm²

This option is incorrect because the area of 18π cm² would imply a radius greater than that which can fit inside the rectangle. To achieve this area, the radius would need to be 9 cm, which exceeds the maximum allowed by the rectangle's dimensions.

B) 16π cm²

This is the correct answer as it is derived from the radius of the largest circle that can fit inside the rectangle. With a diameter equal to the shorter side of the rectangle (8 cm), the radius is 4 cm, and the area is calculated using the formula A = πr², resulting in 16π cm².

C) 8π cm²

This option is incorrect because the area of 8π cm² corresponds to a radius of 4 cm, which is not the maximum radius that can fit within the rectangle. The largest circle would require a radius of 4 cm, leading to an area of 16π cm² instead.

D) 10π cm²

This option is also incorrect, as an area of 10π cm² would suggest a radius of approximately 5.64 cm. This radius cannot fit inside the rectangle since the maximum diameter available is only 8 cm.

Conclusion

The correct answer, 16π cm², accurately reflects the area of the largest circle that can fit inside the given rectangle by utilizing the shorter dimension for its diameter. All other options represent areas that correspond to circles with radii exceeding the rectangle's constraints or underrepresenting the maximum area achievable.