The volume of the sphere is calculated by radius measurement of this spatial geometric figure. The radius of the sphere corresponds to the distance between the center and any point on the figure's surface.
Remember that the sphere is a spatial figure formed by a closed surface where all points are equidistant from the center.
This geometric solid is very present in our daily lives. For example, a ball, a melon, a watermelon, an orange, a Christmas ornament, they are all spherical figures.
It is worth noting that the volume of a figure is usually given in cubic units: cm3m3, etc.
Formula: How to Calculate?
To calculate the volume of the sphere, use the following formula:
Vand = 4.п.r3/3
Where:
Vand: sphere volume
π (Pi): 3.14
r: lightning
Want to know more? See too:
- The Sphere in Spatial Geometry
- Sphere Area
- Spatial Geometry
Example: Solved Exercise
A spherical reservoir has an internal radius of 2m. How many liters of gas fit in this reservoir? Use the value of π = 3.14.
Vand = 4.π.r3/3
Vand = 4/3 π. 23
Vand = 32 π/3 m3
Vand = 32. 3,14/3
Vand = 33, 49 m3
Therefore, this reservoir may contain 33 490 liters of gas.
Entrance Exam Exercises with Feedback
1. (Vunesp-SP) The radius of the base of a cone is equal to the radius of a sphere of 256π cm2 of area. The generator of the cone is 5/4 of the radius. The ratio between the volume of the cone and the volume of the sphere is:
a) 2/32
b) 3/32
c) 6/32
d) 12/32
e) 18/32
Alternative c
2. (UF-CE) A straight circular cylinder Ç tall H and base radius r has the same volume as a sphere s of radius h/2. So the radius of the cylinder is:
a) h/√6
b) h/√5
c) h/3
d) h/4
e) h/√ 2
Alternative to
3. (PUC-RS) If V is the volume of the straight circular cone of radius R and the height R and W is the volume of the ray hemisphere R, so the V/W ratio is:
a) 1/4
b) 1/2
c) 3/4
d) 1
e) 4/3
Alternative b
4. (UF-CE) A vessel in the form of a straight circular cylinder has a base radius of 5 cm, a height of 20 cm and contains water up to a height of 19 cm (neglect the thickness of the vessel walls). Tick the alternative that contains the largest number of steel balls, each with a radius of 1 cm, that we can place in the vase so that the water does not overflow.
a) 14
b) 15
c) 16
d) 17
e) 18
Alternative and
5. (EU-CE) A sphere, with a radius measuring 5 cm, is circumscribed to a straight circular cylinder whose height measures 8 cm. it was called X the ratio between the volume of the sphere and the volume of the cylinder. Among the options below, tick the one with the closest value to X:
a) 1.71
b) 1.91
c) 2.31
d) 3.14
Alternative c
