Answer:
The volume of the sphere is 20 m
Step-by-step explanation:
Given
Solid Shapes: Cylinder and Sphere
Volume of the cylinder [tex]= 30m^3[/tex]
Required
Volume of the sphere
First, we need to calculate the radius of the cylinder
The formula goes thus
[tex]V = \pi r^2h[/tex]
By substituting 30 for V, we have
[tex]30 = \pi r^2h[/tex]
Divide through by h
[tex]\frac{30}{h} = \frac{\pi r^2h}{h}[/tex]
[tex]\frac{30}{h} = \pi r^2[/tex]
Calculating the volume of the sphere
The formula goes thus
[tex]V = \frac{4}{3}\pi r^3[/tex]
Expand Expression
[tex]V = \frac{4}{3} * \pi r^2 * r[/tex]
Substitute [tex]\frac{30}{h} = \pi r^2[/tex]
[tex]V = \frac{4}{3} * \frac{30}{h} * r[/tex]
Simplify Expression
[tex]V = \frac{4}{1} * \frac{10}{h} * r[/tex]
[tex]V = \frac{40}{h} * r[/tex]
Given that the height of the cylinder and the sphere are equal
This means that the height of the cylinder equals the diameter of the sphere.
Mathematically; This is represented by
h = D
Where D represents diameter of the sphere
Recall that D = 2r (2 * radius)
Substitute 2r for D
h = 2r
Substitute h = 2r in [tex]V = \frac{40}{h} * r[/tex]; This gives
[tex]V = \frac{40}{2r} * r[/tex]
[tex]V = \frac{40r}{2r}[/tex]
[tex]V = 20[/tex]
Hence, the volume of the sphere is 20 m
