Mathematics Problems

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

What is the intersection of a sphere and a plane passing through its center?

What is the portion of a sphere bounded by a spherical polygon and the planes of its sides?

What is the portion of a sphere generated by the revolution of a circular sector about any diameter of the circle?

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

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

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

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

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

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

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

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

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?

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

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?

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?

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

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

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

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

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?

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

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

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

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

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

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?

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?