Mathematics Problems

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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?

spherical wedge Signup and view all the answers

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

spherical segment Signup and view all the answers

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

lune 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?

parallel Signup and view all the answers

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

oblique Signup and view all the answers

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

dihedral angle Signup and view all the answers

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

circle 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?

spherical excess Signup and view all the answers

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

polyhedral angle 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?

11 Signup and view all the answers

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

149.08 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?

573.26 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?

71.28 m² 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?

20:25 Signup and view all the answers

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

15.59 cm 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?

75°31' 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?

3.14 m 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?

1496 in2 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?

4000π Signup and view all the answers

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

282.8 Signup and view all the answers

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

6 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?

17,280 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?

9 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?

54 degrees 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?

44 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?

48,000π 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?

0.828 Signup and view all the answers