Plane Geometry

how can I derive the formula of the spherical cap?

A rectangular container, with a height of 24 in., contains 44.9 gal of water when it is full. A stick is placed diagonally from one corner of the upper base as shown. If BC = 10in., AC= 25in. and is a point indicating the water level, find the height and volume of the liquid in the container.

A 3-inch diameter hole is drilled 6 inches deep into the center and normal to the top face of a brass cube 8 inches on a side. The hole is filled with lead. If the brass weighs 525lb/ft^3 and the lead weighs 705lb/ft^3 Find the total mass of two metals.

PS: I can't imagine the drawing.

A chemical plant requires a water supply of 12m^3/hr. Suppose the rate of flow in the water pipe is 2m/sec. Find the radius of the pipe to be used in centimeters.

A cylindrical gas bottle has internal dimensions of 18cm in diameter and 49cm in height. It is designed to contain compressed oxygen gas. The bottle has a mass of 1.75kg when empty and 3.15kg when full of oxygen gas. What is the density of the oxygen gas in a full bottle in kg/m^3?

A plane is passed through a parallelepiped, cutting all the lateral edges and forming a right section which is square. If the lateral area of the solid is 216cm^2 and a lateral edge measures 9cm, find the measure of one side of the right section.

The area of the diagonal section of a cube i equal to 36squareroot of 2. Determine the measures of the edge and the diagonal of the cube.

find the area and volume of the figure developed by an equilateral triangle with sides s if it is revolved about one of its sides.