Ball is roughly the shape of an ordinary tennis ball or soccer ball. The shape is so common in nature, from the shape of planets and stars to tiny water droplets. It also has meaning in engineering and the natural sciences. Therefore, it is important to know the properties of spheres and to measure them. Volume is one such attribute.
Mathematically, the sphere is defined as the area created by the set of points that are a constant distance from a fixed point in space, where the constant pit is known as the center and the distance from the center to the surface as. known is radius. Any object that has the property mentioned above is said to have a spherical shape. If the inside of the sphere is empty, one speaks of a spherical shell or a hollow sphere. If the inside of the sphere is filled, one speaks of a solid sphere.
Volume of a sphere - formula
The volume of a sphere results from the formula:
This formula was first derived from Archimedes, where a sphere occupies 2/3 the volume of a circumscribed cylinder. A hemisphere is half of a complete sphere and the volume of a hemisphere is half of the sphere. Hence the volume of the hemisphere is given by the formula,
Volume of a hemisphere - formula
These formulas are obtained through integration methods. Consider a sphere of radius r centered at the origin of the coordinate axes as shown above. A small incremental distance in the x-direction is given by dx. A plate of thickness dx has an approximately cylindrical shape with a radius y. The volume of the cylinder can be given as (dV) = πy ^ 2 dx. Hence the volume of the sphere is given by the integral within the limits of the radius,
In order to determine the volume of the sphere, only one dimension of the sphere needs to be known, namely the radius of the sphere. If the diameter is known, the radius can easily be calculated using the relationship D = 2r. After finding the radius, use the formula derived above.
How to find the volume of a sphere: example
- The radius of a sphere is 10cm. What is the volume of the sphere?
The radius is indicated. Therefore, the volume of the sphere can be calculated as follows:
How to find the volume of a hemisphere: example
- A spherical water tank has a diameter of 5 m, if the water is filled with an amount of 5 l -1 . If the tank was half full at the beginning, how long does it take to fill the tank completely?
The problem needs to be resolved in two simple steps. First we need to find the empty volume at the beginning and then find out the time it takes to fill that volume. The tank is initially half full. Therefore we have to calculate the volume of a hemisphere, which is also the volume filled with water.