Question

能容纳一个半径为 $4$ 的圆的最小正方形的面积是

The area of the smallest square that will contain a circle of radius $4$ is

$8$

$16$

$32$

$64$

$128$

可以把圆内切在正方形中，使它与正方形四边的中点相切。

因此正方形边长是圆半径的两倍，即 $2 \cdot 4 = 8$ 。

正方形面积为 $8^2 = 64.$

所以正确答案是 D。

We can inscribe the circle inside the square so that it is tangent to the midpoints of each side of the square.

This means that the side length of the square is two times the radius of the circle, making it $2 \cdot 4 = 8.$

Then the area of the square is $8^2 = 64.$

Thus, D is the correct answer.