GEOMETRY TOPIC TEST MU ALPHA THETA 2007 1) What is the length of the longest diagonal of a cube with side length 2? A) 4 B) 8 C) 2 2 D) 2 3 E) NOTA 2) What is the area of a circle with circumference 4π? A) 4π B) 2π C) 4 D) π/4 E) NOTA 3) What is the sum of the exterior angles of a nonagon? A) 180 B) 240 C) 1024 D) 720 E) NOTA 4) Angles Z and Y are supplementary and 4Z = 2Y. Angles U and V are complementary and 8U = V. Which one of the four angles Z, Y, U, or V is the smallest angle? A) Z B) Y C) U D) V E) NOTA 5) What is the geometric mean of 12 and 4? A) 48 B) 4 3 C) 8 D) 24 E) NOTA 6) What is the area of a triangle with sides of length 3, 5, and 6? A) 4 14 B) 56 C) 2 14 D) 28 E) NOTA 7) What is the volume of a square pyramid with base length 3 and height 4? A) 6 B) 12 C) 36 D) 18 E) NOTA 8) If the diameter of a sphere is equal to 6, what is the volume of the sphere? A) 36π B) 48π C) 108π D) 48 E) NOTA
9) What is the length of the hypotenuse of a right triangle with legs length 3 and 3 3? A) 9 B) 12 C) 8 D) 10 E) NOTA 10) What is the area of a parallelogram with base length 6 and height 3? A) 9 B) 10 C) 18 D) 12 E) NOTA 11) What is the volume of a circular cone with base radius 2 and height 3? A) 6π B) 3π C) 2π D) 4π E) NOTA 12) What is the distance between the points (0,0) and (3,4)? A) 7 B) 4/3 C) 4 D) 5 E) NOTA 13) If a right triangle has an angle of 45 and hypotenuse length 5 2, what is the area of the triangle? A) 10 2 B) 12 C) 25 D) 25/2 E) NOTA 14) What is the equation of the line that contains the points (2,4) and (3,5)? A) y = 2x + 4 B) y = 2x + 3 C) y = x + 3 D) y = x + 2 E) NOTA 15) If a square has side length 1 and another square has side length twice that of the first square then what is the ratio of the area of the smaller square to the area of the larger square? A) 4:1 B) 1:2 C) 1:4 D) 2:1 E) NOTA 16) What is the total surface area of a cube with side length 6? A) 36 B) 216 C) 72 D) 48 E) NOTA 17) What is the volume of a sphere with surface area 16π? A) 16π B) 32π/3 C) 32π D) 16π/3 E) NOTA
18) If a circle is inscribed within a square of side length 4 what is the area of the circle? A) 2π B) 4π C) 8π D) 16π E) NOTA 19) What is the area of an equilateral triangle with side length 6? A) 18 B) 36 C) 9 D) 18 3 E) NOTA 20) There is an equilateral triangle inscribed inside a circle with radius 2. What is the area of the triangle? A) 3 3 B) 2 3 C) 4 3 D) 3 E) NOTA 21) There is an equilateral triangle with side length 6. If there is a circle inscribed inside the triangle what is the area of the circle? A) π B) 6π C) 12π D) 3π 3 E) NOTA 22) What is the area of a circle with equation of x 2 + 2x + y 2 + 1 + 4y = 0? A) 2π B) 16π C) π D) 9π E) NOTA 23) What is the area of an equilateral triangle with height 9? A) 81 3 B) 9 3 C) 36 3 D) 27 3 E) NOTA 24) What is the center and radius of the following circle? x 2 + 2x + y 2 + 4y + 1 = 0 A) center = (1,2) r= 4 B) center = (1,-2) r=4 C) center = (-2,1) r = 4 D) center = (-1,-2) r= 4 E) NOTA 25) If two circles are concentric and if a chord of the larger circle is tangent to the smaller circle and has length 10, then what is the area of the annulus formed by the two circles? A) 10π B) 25π C) 5π D) 12.5π E) NOTA
26) What is the area of a regular hexagon with an inscribed circle with radius 9? 243 3 A) 162 3 B) 81 3 C) 27 3 D) E) NOTA 2 27) There is a circle circumscribed about a regular hexagon with side length 6. What is the area of the circle? A) 6π B) 12π C) 36π D) 6π 3 E) NOTA 28) What is the perimeter of an equilateral triangle with area 9 3? A) 27 B) 16 C) 9 3 D) 9 E) NOTA 29) If a triangle has side lengths 4 and 7, then which of the following is a possible value for the third side? A) 11 B) 5 C) 12 D) 3 E) NOTA 30) Seven seventh graders are trying to fit a flagpole of length 2 29 inside of a rectangular prism with dimensions x, x + 2, x + 4. What is the minimum possible dimension of the rectangular prism? A) 2 x 4 x 6 B) 3 x 5 x 7 C) 1 x 3 x 5 D) 4 x 6 x 8 E) NOTA 31) What is the volume of a cone with diameter 10 and slant height 13? A) 100π B) 325π 3 1300π C) 3 D) 400π E) NOTA 32) How many points (x, y) are there in the xy-plane with a distance of 13 from the origin that have integer coordinates? A) 0 B) 4 C) 2 D) 6 E) NOTA 33) A wheel has diameter 40. How far will it roll if it turns 4π radians? A) 50π B) 100π C) 80π D) 75π E) NOTA
34) The perimeters of an equilateral triangle and a square are equal in length. What is the ratio of their areas? A) 4 3 :9 B) 4: 3 C) 6 3 : 5 2 D) 2 3 :9 E) NOTA 35) How many triangles with positive area are there whose vertices are points in the xy-plane whose coordinates are integers (x, y) satisfying 1 < x < 4 and 1 < y < 4? A) 496 B) 512 C) 516 D) 560 E) NOTA 36) If a circle is inscribed in a triangle with sides 10, 24, 26 what is the area of the circle? A) 169π B) 144π C) 676π D) 100π E) NOTA 37) An equilateral triangle has side length 12. A circle is inscribed within the equilateral triangle and another equilateral triangle inscribed within that circle. What is the area of the smaller equilateral triangle? A) 9 3 B) 36 3 C) 18 D) 36 E) NOTA 38) Point D is on side CB of triangle ABC. Angle CAD = angle DAB = 60 degrees, AC = 3 and AB = 6, what is the length of AD? A) 3.5 B) 2.5 C) 3 D) 2 E) NOTA 39) How many non-congruent right triangles are there such that the perimeter in cm and area in cm 2 are numerically equal? A) None B) 1 C) 2 D) 4 E) NOTA 40) The sum of the areas of all the faces of a rectangular solid is 22 cm 2, and the sum of the lengths of all its edges is 24 cm. What is the length in cm of any one of its internal diagonals? A) 11 B) 12 C) 13 D) 14 E) NOTA
Answers: 1. D 2. A 3. E 360 4. C 5. B 6. C 7. B 8. A 9. E 6 10. C 11. D 12. D 13. D 14. D 15. C 16. B 17. B 18. B 19. E 9 3 20. A 21. C 22. E 4π 23. D 24. E center = (-1,-2) r = 2 25. B 26. A 27. C 28. E 18 29. B 30. D 31. A 32. E 8 33. C 34. A 35. C 36. A 37. A 38. D 39. E infinitely many
40. D