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Sagot :
Answer:
134.04 cubic units
Step-by-step explanation:
Step 1
Find the Volume of the Sphere
Formula = 4/3πr³
r= radius = 4
Hence,
Volume = 4/3 × π × 4³
= 268.08 cubic units
Step 2
Find the Volume of the cylinder
Formula = πr²h
r = radius = 4
h = Height = Diameter of the sphere
Radius of a sphere = 4
Diameter = Height of cylinder = 2 × r = 2 × 4 = 8
Hence: π × 4² × 8
= 402.12 cubic units
Step 3
The expression that describes the volume of the cylinder that is not occupied by the sphere = Volume of Cylinder - Volume of sphere
= 402.12 cubic units - 268.08 cubic units
= 134.04 cubic units
The expression that describes the volume of the cylinder that is not occupied by the sphere is 134.04 cubic units
We have given radius of sphere is 4
What is the formula for volume of the Sphere?
[tex]V= 4/3\pi r^3[/tex]
r= radius
We have given that r=4
[tex]Volume = 4/3 \times \pi \times 4^3[/tex]
V= 268.08 cubic units
What is the formula for volume of the cylinder?
[tex]Formula = \pi r^2h[/tex]
r = radius = 4
h = Height = Diameter of the sphere
Radius of a sphere = 4
Diameter = Height of cylinder
= 2 × r
= 2 × 4
= 8
Therefore we get
[tex]V=\pi \times 4^2 \times 8[/tex]
V= 402.12 cubic units
The expression that describes the volume of the cylinder that is not occupied by the sphere = Volume of Cylinder - Volume of sphere
= 402.12 cubic units - 268.08 cubic units
= 134.04 cubic units
Therefore the expression that describes the volume of the cylinder that is not occupied by the sphere is
(402.12 - 268.08) cubic units.
To learn more about the volume visit:
https://brainly.com/question/1972490
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