The volume of the solid generated by the revolution is 33.5 cubic units.
Step-by-step explanation:
It is given that, the diameter of the semi-circle is 4 and it is rotated to one full rotation around its diameter.
A solid generated when a semicircle is being rotated about its diameter is called a "SPHERE".
Therefore, the volume of the solid generated by the revolution is the volume of the sphere.
The formula for volume of the sphere is given by,
Volume of sphere = (4/3)πr³
where, r is the radius and π has the default value of 3.14
Here, the given diameter is 4.
To find the radius = diameter/2
radius = 4/2 = 2.
Now, to calculate volume of sphere substitute r=2 and π=3.14
volume of the sphere = (4/3)×3.14×2³
⇒ (4/3)×3.14×8
⇒ 100.48 / 3
⇒ 33.49 (approximately 33.5)
Therefore, the volume of the solid generated by the revolution is 33.5 cubic units.
