Mathematics Problems
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Questions and Answers

What is the shape of a solid bounded by a surface where all points are equidistant from a central point?

  • sphere (correct)
  • hyperboloid
  • paraboloid
  • ellipsoid
  • What is the intersection of a sphere and a plane passing through its center?

  • small circle
  • half circle
  • great circle (correct)
  • poles of a circle
  • What is the portion of a sphere bounded by a spherical polygon and the planes of its sides?

  • spherical segment (correct)
  • spherical wedge
  • spherical pyramid
  • spherical sector
  • What is the portion of a sphere generated by the revolution of a circular sector about any diameter of the circle?

    <p>spherical wedge</p> Signup and view all the answers

    What is the portion of a sphere included between two parallel planes?

    <p>spherical segment</p> Signup and view all the answers

    What is the shape of the portion of a sphere lying between two semi-circles of great circles?

    <p>lune</p> Signup and view all the answers

    What is the relationship between a line and a plane when they do not meet, no matter how far they are produced?

    <p>parallel</p> Signup and view all the answers

    What is the term for a line that meets a plane but is not perpendicular to it?

    <p>oblique</p> Signup and view all the answers

    What is the term for the opening between two intersecting planes?

    <p>dihedral angle</p> Signup and view all the answers

    What is the shape of the intersection of a plane and a sphere?

    <p>circle</p> Signup and view all the answers

    What is the term for the excess of the sum of the interior angles of a polygon over (n-2)180 degrees?

    <p>spherical excess</p> Signup and view all the answers

    What is the term for the opening where three or more planes meet at a common point?

    <p>polyhedral angle</p> Signup and view all the answers

    In a polygon, if the interior angles are in arithmetic progression, the least angle is 120° and the common difference is 5°, what is the number of sides?

    <p>11</p> Signup and view all the answers

    What is the perimeter of a regular dodecagon inscribed in a circle of radius 24?

    <p>149.08</p> Signup and view all the answers

    What is the area inside and concentric to a larger pentagon but outside of a smaller pentagon, if the larger pentagon has sides of 20 cm and the smaller pentagon has sides of 10 cm?

    <p>573.26</p> Signup and view all the answers

    What is the area of the part not covered by a regular five-pointed star touching its circumference in a circle with a diameter of 10 m?

    <p>71.28 m²</p> Signup and view all the answers

    What is the ratio of the bases of a trapezoid, if it has an area of 360 m² and an altitude of 20 m?

    <p>20:25</p> Signup and view all the answers

    What is the length of the diagonal of a cube with a volume of 729 cubic cm?

    <p>15.59 cm</p> Signup and view all the answers

    What is the angle at which an element of a right circular cone is inclined to the base, if the lateral area is 4 times the area of the base?

    <p>75°31'</p> Signup and view all the answers

    At what height from the table should a sphere and a right circular cone be cut to have equal circular sections?

    <p>3.14 m</p> Signup and view all the answers

    What is the surface area of a right circular cone with a radius of 14 inches and a slant height of 20 inches?

    <p>1496 in2</p> Signup and view all the answers

    What is the volume of a sphere with a zone of a spherical segment having an area of 180π m2 and a volume of 468π m3?

    <p>4000π</p> Signup and view all the answers

    What is the area of a regular octagon inscribed in a circle of radius 10 inches?

    <p>282.8</p> Signup and view all the answers

    What is the number of sides of a polygon with a sum of interior angles of 540∘?

    <p>6</p> Signup and view all the answers

    If an air conditioner changes the air once every five minutes, how many cubic feet of air does it change per hour?

    <p>17,280</p> Signup and view all the answers

    If the sum of the interior angles of a polygon of n sides is 1080 degrees, what is the value of n?

    <p>9</p> Signup and view all the answers

    What is the spherical excess of a spherical polygon of four sides whose angles are 95 degrees, 112 degrees, 134 degrees, and 78 degrees?

    <p>54 degrees</p> Signup and view all the answers

    If a rectangle is inscribed in a circle whose radius is 5 inches, and the base of the rectangle is 8 inches, what is the area of the rectangle?

    <p>44</p> Signup and view all the answers

    If three spheres of radii 10, 20, and 30 cm respectively are melted and formed into a single sphere, what is the volume of the single sphere?

    <p>48,000π</p> Signup and view all the answers

    If the corner of a 2-meter square is cut off to form a regular octagon, what is the length of the resulting side of the octagon?

    <p>0.828</p> Signup and view all the answers

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