Tennis balls are stacked four high in a rectangular prism package. The diameter of one ball is 6.5cm. a) Calculate the volume of the...

The  diameter of the balls =6.5cm. Each  rectangular prism
shaped pack contains 4 tennis balls kept high one over the other . So house the
arrangement the required(inner dimension of the pack = 6.5 cm length , 6.5 cm width and
6.5*4 = 26cm high.

a) the volume of the rectangular prism =
length*length*height = 6.5^2*(6.5*4) =1098.5 cm^3.

b)The
(minimum )amount of material to make the fixed shape is (prportional)  equal to the area
of the 6 surface of the rectangular box= 2(lw+lh+wh) = 2(3w^2+2w^2), as l=w and h =
2w .  So the surface area = 10*6.5^2 = 422.5 sq cm.

The
minimum material to cover the 4 balls to keep in the fixed stack   shape  does not
arise.

c)

The amount of empty
space in the box = Volume of the rectangular prism - volume of the 4 boxes = 6.5*2*26 -
2*(4/3)(Pi*r^3^2) = 1098.5 - 2*(4/3)pi(6.5/21006.96)^3 = 523.33
cm^3.

d) We assumed that the material is (proportional)
equal  to the area of the surface .