Cuprins
In this publication, we will consider formulas that can be used to calculate the volume of a spherical layer (slice of a ball), as well as an example of solving a problem to demonstrate their practical application.
Definiția unui strat sferic
Strat sferic (sau felie de minge) – aceasta este partea care rămâne între două plane paralele care o intersectează. Poza de mai jos este colorată în galben.
- R este raza mingii;
- r1 este raza primei baze tăiate;
- r2 este raza celei de-a doua baze tăiate;
- h este înălțimea stratului sferic; perpendicular de la centrul primei baze pe centrul celei de-a doua.
Formula for finding the volume of a spherical layer
To find the volume of a spherical layer (slice of a ball), you need to know its height, as well as the radii of its two bases.
The same formula can be presented in a slightly different form:
note:
- if instead of base radii (r1 и r2) their diameters are known (d1 и d2), the latter must be divided by 2 to obtain their corresponding radii.
- număr π de obicei rotunjite la 3,14.
Exemplu de problemă
Find the volume of a spherical layer if the radii of its bases are 3,4 cm and 5,2 cm, and the height is
Soluţie
All we need to do in this case is to substitute the known values into one of the formulas above (we will choose the second one as an example):
