For a triangle of given three sides, say a, b, and c, the formula for the area is given by
where s is the semi perimeter equal to P/2 = (a + b + c)/2.
Ptolemy's theorem for cyclic quadrilateral states that the product of the diagonals is equal to the sum of the products of opposite sides. From the figure below, Ptolemy's theorem can be written as
For a cyclic quadrilateral with given sides a, b, c, and d, the formula for the area is given by
Where s = (a + b + c + d)/2 known as the semi-perimeter.
Problem 001
A 523.6 cm3 solid spherical steel ball was melted and remolded into a hollow steel ball so that the hollow diameter is equal to the diameter of the original steel ball. Find the thickness of the hollow steel ball.
Problem 001
A certain wire that weighs 8.5 g/cc has a total mass of 155 kg.
The total surface area of the sphere is four times the area of great circle. To know more about great circle, see properties of a sphere. Given the radius r of the sphere, the total surface area is
For detailed information about sphere, see the Solid Geometry entry, The Sphere.
The formula for the volume of the sphere is given by
