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a cylinder with a height of 17 centimeters and a radius of 8 centimeters is filled with water. if the water is then poured into the rectangular prism shown, will it overflow? write an argument that can be used to defend your solution.

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Answer:

The volume of a cylinder is calculated by multiplying the area of the base by the height. The area of the base of a cylinder is πr², where r is the radius of the cylinder. In this case, the radius is 8 centimeters, so the area of the base is 201.06 cm². The height of the cylinder is 17 centimeters, so the volume of the cylinder is 3417.02 cm³.

The volume of a rectangular prism is calculated by multiplying the length, width, and height. In this case, the length is 15 centimeters, the width is 12 centimeters, and the height is 9 centimeters. The volume of the rectangular prism is 1620 cm³.

Since the volume of the cylinder is less than the volume of the rectangular prism, the water will not overflow.

Here is an argument that can be used to defend this solution:

The volume of the cylinder is calculated by multiplying the area of the base by the height.

The area of the base of a cylinder is πr², where r is the radius of the cylinder.

In this case, the radius is 8 centimeters, so the area of the base is 201.06 cm².

The height of the cylinder is 17 centimeters, so the volume of the cylinder is 3417.02 cm³.

The volume of a rectangular prism is calculated by multiplying the length, width, and height.

In this case, the length is 15 centimeters, the width is 12 centimeters, and the height is 9 centimeters.

The volume of the rectangular prism is 1620 cm³.

Since the volume of the cylinder is less than the volume of the rectangular prism, the water will not overflow.

Explanation:

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