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SAT Topic Tests

Geometry And Measurement - Advanced

         

In the figure above, a regular polygon has been shaded grey, and partially covered by a piece of paper. If \( s + t = 40 ^ \circ \), how many sides does the regular polygon have?

A) 6
B) 10
C) 12
D) 15
E) 18

In the \(xy\) coordinate plane, how many points are at distance of exactly \(5\) units from the origin?

A) 1
B) 4
C) 8
D) 12
E) Strictly more than 12

A sphere of radius \(r\) is tangential to all 6 faces of a cube with side length \(s\). What is the volume of the sphere in terms of \(s\)?

A) \( \pi s^3 \)
B) \( \frac{1}{3} \pi s^3 \)
C) \( \frac{ 1}{6} \pi s^3 \)
D) \( \frac{ 1}{8} \pi s^3 \)
E) \( \frac{4}{3} \pi s^3 \)

In the above figure, the circle circumscribes square \(ABCD\). What is the degree measure of arc \( \widehat{BC} \)?

A) \( 30 ^ \circ \)
B) \( 45 ^ \circ \)
C) \( 60 ^ \circ \)
D) \( 90 ^ \circ \)
E) \( 180 ^ \circ \)

In the above figure, there are 25 congruent right angled isosceles triangles. If the area of \( \triangle DFH \) is 100, what is the area of \( \triangle AFK \)?

A) 100
B) 400
C) 525
D) 600
E) 625

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