Download 2011GeminiRound3Test - Rocket City Math League

Name________________________________________
Rocket City Math League
2011-2012
Round 3
Gemini Test
Answers must be written inside the adjacent answer boxes. All answers must be written in exact, reduced, simplified, and rationalized form.
No calculators, books, or other aides may be used.
1. An angle measures 24 less than half of its supplement. What is the measure of the angle?
(1 point)
2. The surface areas of two similar spheres are 121 and 289, what is the ratio of the volume of the smaller to the
volume of the larger?
(1 point)
3. What is the sum of the measures of the interior angles in Moogle’s 52-gon?
4. Solve for x in the given figure. Line A is perpendicular to lines C,
D, E, and F. The distance on line B between lines C and D is 2,
the distance on line B between lines D and E and E and F is 3/2,
the distance on line A between D and E is 2/3, and the distance
on line A between C and D is x.
C
D
E
(1 point)
B
A
F
(1 point)
5. Glov’s triangle ACB is inscribed in a circular space ring as shown.
CB is 120 degrees, AB is a diameter with length 10, and
the length of AC is 5, find the area of Glov’s triangle.
If minor arc
(2 points)
6. A regular figure is drawn such that the sum of the measures of its interior angles is 720º. If one of its sides
measures 2 cm, what is the area of the figure in square centimeters?
(2 points)
7. Glob is given a string of 15 feet, and he creates an equilateral triangle with sides formed by the string. What is
the distance from the centroid of the triangle to one side of his triangle?
(2 points)
8. A cube has a cylinder inscribed in it. If the radius of the cylinder is 2 cm, find the ratio of the number of cubic
centimeters in the volume of the region outside the cylinder but inside the cube to the number of square centimeters
in the total surface area of the cylinder.
(3 points)
9. Oogla’s giant space cone with a volume of 100 km3 and a height of 30 km has been damaged and repaired
repeatedly, lowering the height of the cone while not changing the cone’s radius. If the height of the cone is
decreased by 10 km, then what is its resulting volume in cubic kilometers?
(3 points)
10. Two circles with radii 3 and 2 have centers that are 10 units apart. Find the positive difference between the
length of one of the common internal tangents and the length of one of the common external tangents to the two
circles.
(4 points)
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