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Geometry and Measurement

SAT Geometry Word Problems

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The semi-circles in the diagram above are tangent to each other. If \(10\) semi-circles fit on segment \(\overline{AB}\) and if each semi-circle has a diameter of 2, what is the difference between the sum of the lengths of the arcs formed by all the semi-circles and the length of \(\overline{AB}?\)

(A) \(\ \ 0\)
(B) \(\ \ 10(\pi-2)\)
(C) \(\ \ 20\)
(D) \(\ \ 10\pi\)
(E) \(\ \ 20 (\pi - 1)\)

If the area of a wheel is \(100\pi\) ft\(^2,\) how many feet will it travel if it makes \(600\) revolutions?

(A) \(\ \ 10\)
(B) \(\ \ 20 \pi\)
(C) \(\ \ 600\pi\)
(D) \(\ \ 12000\)
(E) \(\ \ 12000 \pi\)

The lengths of two sides of a triangle are \(3\) and \(15.\) If the length of the third side is \(x,\) what are the possible values for \(x?\)

(A) \(\ \ 3 < x < 15\)
(B) \(\ \ 3 < x < 16\)
(C) \(\ \ 11 < x < 17\)
(D) \(\ \ 12 < x < 18\)
(E) \(\ \ 14 < x < 20\)

A circle with radius \(r=3\) overlaps another circle with radius \(R=11.\) If the area of the overlapping region is \(\pi,\) what is the area of the non-overlapping region?

(A) \(\ \ 121 \pi\)
(B) \(\ \ 128\pi\)
(C) \(\ \ 129 \pi\)
(D) \(\ \ 130 \pi\)
(E) \(\ \ 131 \pi\)

A rectangle has length \(18\) and width \(9.\) From each corner, a square with side 1 is cut. What is the perimeter of the new figure?

(A) \(\ \ 27\)
(B) \(\ \ 46\)
(C) \(\ \ 54\)
(D) \(\ \ 158\)
(E) \(\ \ 162\)

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