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# SAT Geometry Word Problems



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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