Three identical circles are tangent to each other externally. If the area of the curvilinear triangle formed by the point of tangency of the three circles is 142 cm², compute the radius of each circle.

Find the area of a regular hexagon inscribed in a circle of radius 1.

The bases of a right prism is a hexagon with one of each side equal to 6 cm. The bases are 12 cm apart. What is the volume of a right prism?

A pyramid has a square base of 8 m on a side and an altitude of 10 m. How many liters of water will it hold when full and inverted?

A right circular cone whose vertical angle is 90 degrees has a diameter of a sphere as its axis and has its vertex on the sphere. Determine the ratio of the volume of the cone to that of the sphere.

Find the area of a triangle with sides equal to 1.017 cm, 2.032 cm, and 2.055 cm, respectively.

A group of children playing with marbles placed 50 pieces of the marbles inside a cylindrical container with water filled to a height of 20 cm. If the diameter of each marble is 1.5 cm and that of the cylindrical container is 6 cm. What would be the new height of water inside the cylindrical container after the marbles were placed inside?

A trapezoid 6 m in altitude have bases of 12 m and 18 m, respectively. If it is divided into two parts by a line parallel to the bases such that the ratio of the areas of the two parts formed is 2:3, compute the length of the dividing line.

A conical vessel has a height of 24 cm. and a base diameter of 12 cm. It holds water to a depth of 18 cm above its vertex. Find the volume of its content.

How many sides has a polygon if the sum of its interior angles equals twice the sum of its exterior angles?