Answer:
C. V = two-thirds (27)
Step-by-step explanation:
Given
Solid Shapes: Cylinder and Sphere
Volume of Cylinder = 27π ft³
Required
Volume of the sphere.
From the question,
<u>We have that</u>
1. The volume of the sphere is the same as the volume of the cylinder
2. The height of the sphere is the same as the height of the cylinder.
From (2) above;
This means that the height of the cylinder equals the diameter of the sphere.
Let h represent the height of the sphere and d represent the diameter of sphere.
Mathematical, d = h
Recall that radius, r =
Substitute h for d in the above expression
. ----- (take note of this)
Calculating the volume of a cylinder.
V = πr²h
Recall that V = 27; This gives us
27 = πr²h
Divide both sides by h
-------------------
Calculating the volume of a sphere
Expand the above expression
Substitute
Recall that
So,
V = two-third (27)