Spherical bodies are of enormous importance in the daily life of various activities. In some sports, the spherical shape is represented by the ball, which is the main object in the progress of soccer, volleyball, basketball, bowling, golf, among other sports. In mobile objects such as bicycles, cars and trucks, the spherical shape is present in mechanical components responsible for the locomotion of such vehicles. In these vehicles, the bearings are formed by balls that allow the rotation of a wheel on an axle to occur. See representative figure of a bearing:
Bearings are also widely used in the industrial sector, facilitating the work of moving machine parts. To analyze how simple objects use the characteristic of spherical bodies, we can take as an example a flask of Roll On deodorant. In these bottles, the transfer of liquid to the skin occurs through a movement performed by a ball.
Due to these numerous uses, the sphere has, according to Mathematics, with regard to Spatial Geometry, Area and Volume that are determined by mathematical algebraic expressions. Look:
Area
A = 4 • π • r2
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Volume
V = 4 • π • r3
3
Mathematical calculations, involving the area and volume of a sphere, cover the measure of the radius, which is the distance between the center of the sphere and its extremity and the constant value of the irrational number π (pi), given by approximately 3,14. See the sphere and its elements:
Example 1
A plastic sphere has a radius measuring 20 centimeters. Determine the area of this spherical region.
A = 4 • π • r2
A = 4 • 3.14 • 202
A = 4 • 3.14 • 400
H = 5,024 cm2
Example 2
A reservoir is spherical in shape with a radius of 15 meters. Calculate the total storage capacity of this reservoir.
V = 4 • π • r3
3
V = 4 • 3,14 • 153
3
V = 4 • 3,14 • 3.375
3
V = 42.390
3
V = 14,130 m3
We have that 1 m³ corresponds to 1000 liters. So 14,130 m³ equals 14,130 000 liters of storage capacity.
by Mark Noah
Graduated in Mathematics
Brazil School Team
Would you like to reference this text in a school or academic work? Look:
RIGONATTO, Marcelo. "Area and Volume of Spherical Bodies"; Brazil School. Available in: https://brasilescola.uol.com.br/matematica/Area-volume-corpos-esfericos.htm. Accessed on June 27, 2021.
Circle Sector, Circle, Circle Area, Circle Sector Area, Bounded Region of a Circle, Radian, Circle Sector Area Demonstration, Circle Segment, Circle Crown.
