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Name________________________________________
Rocket City Math League
2011-2012
Round 2
Gemini Test
Answers must be written inside the adjacent answer boxes. All answers must be written in exact, reduced, simplified, and rationalized form. All
decimals and mixed numbers must be written as improper fractions. No calculators, books, or other aides may be used.
1. If a prism has triangular bases, what is the sum of the number of edges, faces, and vertices?
(1 point)
2. What is the area of Gloob’s square shaped space garden if its diagonal is 5?
(1 point)
3. If a regular polygon has an angle measure of 150 º , what is the sum (in degrees) of the interior angles plus the
sum of the exterior angles (one at each vertex) of the polygon?
(1 point)
4. The paths joining planets Loki, Saluma, and Tiponia make a right triangle when viewed from planet Akadon. If
one angle of this triangle measures thirty degrees and the leg adjacent to that angle measures 7 light years, what is
the length of the hypotenuse (in light years)?
(1 point)
5. In circle O, the length of minor arc AC is 15π with AB as a diameter, and the measure of AOC  150 , what
is the area of sector COB?
C
(2 points)
A
B
6. Mong’s house is a cylinder with a height of 7 and a total surface area of 42π. What is the radius of one of its
bases?
(2 points)
7. Ooma’s space pie is a regular hexagon with an apothem of 3 3 ; find the area of the hexagon.
2
(2 points)
8. Given cyclic quadrilateral ABCD inscribed in circle O with AB = 6, AD = 2 3 ,
B
BC = 6 and DC = 2 3 , find the area of circle O.
A
C
(3 points)
D
9. Line segment AB intersects line segment CD at point E. Find the least possible measure of CEB if


mCEA  8 x 2  12 x  , and mAED  4 x 2  7 x  103 .
(3 points)
10. The volume of a regular tetrahedron is 144 2 . Find the volume of a sphere inscribed inside this regular
tetrahedron.
(4 points)
The material on this page is the property of the Rocket City Math League. Reproduction other than for non-profit educational purposes is strictly prohibited without the
expressed written consent of the RCML.
Rocket City Math League
www.rocketcitymath.org
Sponsored by Mu Alpha Theta - National Math Honor Society
www.mualphatheta.org
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