Question

A tennis ball can in the shape of a right circular cylinder holds three tennis balls snugly. If the radius of a tennis ball is 3.3 ​cm, what percentage of the can is not occupied by tennis​ balls?

Answer 1

Explanation:

1.- Volumeo f the circular cylinder (to holds three balls)

each ball is 3,3 cm radius then is 6,6 cm diameter

Then 3 diameters are equal to 3* 6.6 = 19,8 cm (the height of the cylinder)

Then the volume of the cylinder is

V(c) = π*r²*h ⇒ V(c) =3,14*(3,3)²*19,8 ⇒ V(c) = 677.05 cm³

Now the volume of a tennis ball (is an sphere)

V(s) = 4/3*π*r³ ⇒ V(s) =4/3*3,14 * (3,3)³ ⇒ V(s) = 150,46 cm³

We have three balls then volume of the three balls

150,46*3 = 451.37 cm³

So V(c) = 677,05 cm³ V(bt) = 451,41

V(c) /V(bt) = 677,05/ 451,41 = 1,498

Then V(c) is 49.8 % bigger than of V(bt) of three balls