Mensuration (Areas and Volumes)

Gives the perimeter or boundary length of a circle of radius r.

Gives the total area enclosed by a circle of radius r.

Gives the area of a semicircle of radius r.

Gives the length of an arc subtending angle theta at the centre of a circle of radius r.

Gives the area of a circular sector of radius r with central angle theta.

Gives the total perimeter of a circular sector bounding two radii and the arc.

Gives the area of a minor segment subtended by angle theta at the centre of radius r.

Gives the length of a chord subtending central angle theta in a circle of radius r.

Gives the area of a triangle given two adjacent sides and their included angle.

Gives the area of an equilateral triangle with side length a.

Gives the volume of a rectangular cuboid with length l, breadth b, and height h.

Gives the total surface area of all six faces of a cuboid.

Gives the volume of a cube with edge length a.

Gives the total surface area of a cube of edge length a.

Gives the lateral curved surface area of a right circular cylinder of radius r and height h.

Gives the total surface area of a solid right circular cylinder.

Gives the volume enclosed by a right circular cylinder of radius r and height h.

Gives the volume of material in a hollow circular cylinder with outer radius R and inner radius r.

Relates the slant height l of a right circular cone to its base radius r and vertical height h.

Gives the curved surface area of a right circular cone of radius r and slant height l.

Gives the sum of the curved surface area and circular base area of a cone.

Gives the volume of a right circular cone of base radius r and height h.

Gives the surface area of a sphere of radius r.

Gives the volume enclosed by a sphere of radius r.

Gives the curved surface area of a hemisphere of radius r.

Gives the total surface area of a solid hemisphere including its flat circular base.

Gives the volume of a hemisphere of radius r.

Gives the slant height of a conical frustum with base radii R and r and vertical height h.

Gives the curved lateral surface area of a conical frustum with radii R, r and slant height l.

Gives the volume of a right circular conical frustum of height h and base radii R, r.