30 Questions
What is the shape of a solid bounded by a surface where all points are equidistant from a central point?
sphere
What is the intersection of a sphere and a plane passing through its center?
great circle
What is the portion of a sphere bounded by a spherical polygon and the planes of its sides?
spherical segment
What is the portion of a sphere generated by the revolution of a circular sector about any diameter of the circle?
spherical wedge
What is the portion of a sphere included between two parallel planes?
spherical segment
What is the shape of the portion of a sphere lying between two semi-circles of great circles?
lune
What is the relationship between a line and a plane when they do not meet, no matter how far they are produced?
parallel
What is the term for a line that meets a plane but is not perpendicular to it?
oblique
What is the term for the opening between two intersecting planes?
dihedral angle
What is the shape of the intersection of a plane and a sphere?
circle
What is the term for the excess of the sum of the interior angles of a polygon over (n-2)180 degrees?
spherical excess
What is the term for the opening where three or more planes meet at a common point?
polyhedral angle
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?
11
What is the perimeter of a regular dodecagon inscribed in a circle of radius 24?
149.08
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?
573.26
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?
71.28 m²
What is the ratio of the bases of a trapezoid, if it has an area of 360 m² and an altitude of 20 m?
20:25
What is the length of the diagonal of a cube with a volume of 729 cubic cm?
15.59 cm
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?
75°31'
At what height from the table should a sphere and a right circular cone be cut to have equal circular sections?
3.14 m
What is the surface area of a right circular cone with a radius of 14 inches and a slant height of 20 inches?
1496 in2
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?
4000π
What is the area of a regular octagon inscribed in a circle of radius 10 inches?
282.8
What is the number of sides of a polygon with a sum of interior angles of 540∘?
6
If an air conditioner changes the air once every five minutes, how many cubic feet of air does it change per hour?
17,280
If the sum of the interior angles of a polygon of n sides is 1080 degrees, what is the value of n?
9
What is the spherical excess of a spherical polygon of four sides whose angles are 95 degrees, 112 degrees, 134 degrees, and 78 degrees?
54 degrees
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?
44
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?
48,000π
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?
0.828
Solve a variety of math problems, including geometry, trigonometry, and algebra. Test your skills and knowledge in different areas of mathematics. Improve your problem-solving abilities with these challenging questions.
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