What is the area of the largest circle that can fit entirely inside a rectangle measuring 8 centimeters by 10 centimeters?

Rationale

The area of the largest circle that can fit entirely inside a rectangle measuring 8 cm by 10 cm is 16π cm^2.

This is because the diameter of the largest circle that can fit inside the rectangle would be equal to the shortest side of the rectangle, which is 8 cm in this case. Hence, the radius would be 4 cm (half of the diameter). The area of a circle is calculated using the formula πr^2, which gives us 16π cm^2 in this case.

A (18π cm^2) YOUR ANSWER

This is incorrect because the area of the circle cannot exceed the area of the rectangle it is enclosed within. The area of the rectangle is 80 cm^2, and 18π cm^2 is approximately 56.55 cm^2, which is less than the area of the rectangle but larger than the area of the largest possible circle that can fit inside the rectangle.

C (8π cm^2) YOUR ANSWER

This choice is incorrect because it represents the area of a circle with a radius of approximately 2.83 cm. However, the radius of the largest possible circle that can fit inside the rectangle is 4 cm, not 2.83 cm.

D (10π cm^2) YOUR ANSWER

This choice is incorrect as it represents the area of a circle with a radius of approximately 3.18 cm. However, the radius of the largest possible circle that can fit inside the rectangle is 4 cm, not 3.18 cm.

Conclusion

The area of the largest circle that can fit entirely inside a rectangle is determined by the shortest side of the rectangle, which acts as the diameter of the circle. In this case, the shortest side of the rectangle is 8 cm, making the radius of the circle 4 cm. Therefore, applying the formula for the area of a circle (πr^2), we find that the largest possible area of a circle that can fit inside this rectangle is 16π cm^2.

What is the area of the largest circle that can fit entirely inside a rectangle measuring 8 centimeters by 10 centimeters?

The area of the largest circle that can fit entirely inside a rectangle measuring 8 cm by 10 cm is 16π cm^2.

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