The radius of the smallest circle that can contain the figure would be the distance from the center of the square to one of its corners. This is because the circle must be large enough to contain the entire square and the semicircle.

Step 1: Find the diagonal of the square. The diagonal of a square can be found using the Pythagorean theorem (a² + b² = c²), where a and b are the sides of the square and c is the diagonal. In this case, the side of the square is 2 cm, so the diagonal is √(2² + 2²) = √8 cm.

Step 2: The diagonal of the square is the diameter of the circle that can contain the square. Therefore, the radius of this circle is half of the diagonal, which is √8/2 = √2 cm.

Step 3: The radius of the smallest circle that can contain the figure is the sum of the radius of the semicircle (which is equal to the side of the square, 2 cm) and the radius of the circle that can contain the square (√2 cm). So, the radius of the smallest circle that can contain the figure is 2 + √2 cm.

None of the options provided (198 cm, 218 cm, 158 cm, 178 cm) match this answer. There might be a mistake in the options or in the question itself.

Question

The radius of the smallest circle that can contain the figure would be the distance from the center of the square to one of its corners. This is because the circle must be large enough to contain the entire square and the semicircle.

Step 1: Find the diagonal of the square. The diagonal of a square can be found using the Pythagorean theorem (a² + b² = c²), where a and b are the sides of the square and c is the diagonal. In this case, the side of the square is 2 cm, so the diagonal is √(2² + 2²) = √8 cm.

Step 2: The diagonal of the square is the diameter of the circle that can contain the square. Therefore, the radius of this circle is half of the diagonal, which is √8/2 = √2 cm.

Step 3: The radius of the smallest circle that can contain the figure is the sum of the radius of the semicircle (which is equal to the side of the square, 2 cm) and the radius of the circle that can contain the square (√2 cm). So, the radius of the smallest circle that can contain the figure is 2 + √2 cm.

None of the options provided (198 cm, 218 cm, 158 cm, 178 cm) match this answer. There might be a mistake in the options or in the question itself.

Knowee AI · Accepted Answer

The radius of the smallest circle that can contain the figure would be the distance from the center of the square to one of its corners. This is because the circle must be large enough to contain the entire square and the semicircle.

Step 1: Find the diagonal of the square. The diagonal of a square can be found using the Pythagorean theorem (a² + b² = c²), where a and b are the sides of the square and c is the diagonal. In this case, the side of the square is 2 cm, so the diagonal is √(2² + 2²) = √8 cm.

Step 2: The diagonal of the square is the diameter of the circle that can contain the square. Therefore, the radius of this circle is half of the diagonal, which is √8/2 = √2 cm.

Step 3: The radius of the smallest circle that can contain the figure is the sum of the radius of the semicircle (which is equal to the side of the square, 2 cm) and the radius of the circle that can contain the square (√2 cm). So, the radius of the smallest circle that can contain the figure is 2 + √2 cm.

None of the options provided (198 cm, 218 cm, 158 cm, 178 cm) match this answer. There might be a mistake in the options or in the question itself.

A semicircle is drawn on one of the sides of the square with the side of the square as the diameter of the circle. If the length of the side of the square is 2 cm, What is the radius of the smallest circle that can contain this figure?Options 198 cm 218 cm 158 cm 178 cm

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