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Figure This!


Complete Solution:

The car wiper cleans a greater area.

The car wiper rotates through 1/4 (or one quarter) of a circle. The area cleaned is the difference in the areas of two quarter-circles as shown below:

The area of a circle may be found using the following formula:

The wiper arm swings through an arc of 90°, or 1/4 of a circle. The area of a quarter-circle can be found by multiplying the area of the corresponding circle by 1/4. In this case, the area cleaned by the wiper is the area of the bigger quarter-circle minus the area of the smaller one. The radius of the big circle is 6 + 12, or 18 inches. The radius of the small circle is 6 inches so that the area cleaned is:

The area of the shape cleaned by the truck wiper is really the same as a rectangle.

The curved area at the top of the shape is the same size as the part at the bottom that is not cleaned by the wiper. The height of the rectangle is determined by the size of the wiper: 12 inches. The width of the rectangle can be found by drawing the figure to scale, then measuring, or by using the Pythagorean theorem. According to the Pythagorean theorem, the sum of the squares of the two shorter sides of a right triangle equals the square of the longest side, thus:

Therefore, the width of the rectangle is the square root of 288, or approximately 17 inches. The area of a rectangle can be found by multiplying its height and its width. In this case, the area is about 17 × 12, or 204 square inches. This is less than the area cleaned by the car wiper.

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