Answer : The correct option is, (A) [tex]54\pi cm^3[/tex]
Step-by-step explanation :
First we have to calculate the volume of cylinder.
Formula used:
Volume of cylinder = [tex]\pi r^2h[/tex]
where,
r = radius = 3 cm
h = height = 18 cm (We are assuming that 3 solid spheres stacked to each other = 3 × diameter of each sphere = 3 × 2 × 3 = 18)
Volume of cylinder = [tex]\pi (3cm)^2\times (18cm)[/tex]
Volume of cylinder = [tex]162\pi cm^3[/tex]
Now we have to calculate the volume of 3 solid spheres.
Formula used:
Volume of 3 spheres = [tex]3\times \frac{4}{3}\pi r^3[/tex]
Volume of 3 spheres = [tex]4\pi r^3[/tex]
Volume of 3 spheres = [tex]4\pi (3)^3[/tex]
Volume of 3 spheres = [tex]108\pi cm^3[/tex]
Now we have to calculate the amount of empty space within a cylinder.
Amount of empty space within a cylinder = Volume of cylinder - Volume of 3 spheres
Amount of empty space within a cylinder = [tex]162\pi cm^3-108\pi cm^3[/tex]
Amount of empty space within a cylinder = [tex]54\pi cm^3[/tex]
Therefore, the amount of empty space within a cylinder is, [tex]54\pi cm^3[/tex]
