Question

Find the amount of empty space within a cylinder containing three solid spheres, where each sphere has a radius of 3 cm. (Volume of a sphere =43πr3)

Answer 1

Answer:

Ves = 169.56 cm³

Step-by-step explanation:

Let call Vc   volume of cylinder

If the cylinder has to contain three spheres of radius 3 cm the height of the

cylinder is  3 * 2 * 3 = 18 cm   ( we have three diameters )

The radius of the base of the cylinder is 3 cm

And Vc = π*r²*h    ⇒ Vc = (3,14) * 9 * 18   ⇒  Vc = 508.68 cm³

On the other hand we have Vs (volume of one sphere)

Vs  = 4/3 * π * r³     ⇒   Vs  = 4/3 * 3,14 * (3)³     ⇒  Vs = 113,04 cm³

as we have 3 spheres the total volume is   3 * 113.04

Vts = (total volume of spheres)  =  339,12 cm³

The empty space withing the cylinder is the difference between Vc and Vts

Ves ( volume of empty space ) =  Vc - Vts   =   508.68  -  339,12

Ves = 169.56 cm³

Answer 2

Step-by-step explanation:

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