Each tennis ball is 2.63 inches in diameter. The cylinder that the tennis balls will be placed in has a diameter of 13 inches and a height of 35 inches. How many tennis balls can fit inside the container? how many more tennis balls could fit into the container if the container's dimensions are doubled? You must show all work to receive credit

Question

alecwilson · Answer

A. Find the volume of a single tennis ball(use Sphere formula)
B. Find the volume of the cylinder that will hold the tennis balls(use cylinder formula)
C. Find the number of tennis balls that should be able to fit inside of the cylinder.

pythagoras123 · Answer

A. 

$$\frac{ 4 }{ 3 }\pi (1.315)^3=?$$   

B. $$\pi (7.5)^2 (35) = ? $$

C. Across the cylinder, we can fit 13/2.63 = 4.94 spheres. We can only fit whole spheres, and we can't fit 5 spheres either. So the maximum number of spheres across is 4. 

From top to bottom of the cylinder, we can fit 35/2.63 = 13.3 spheres. Using the same reasoning as above, we round down to 13 spheres. 

4 columns of spheres x 13 rows of spheres = 52 spheres.

alecwilson · Answer

A=9.525019376?
B=6185.010537
and C is 52 Tennis balls?
@pythagoras123

pythagoras123 · Answer

Yes, if you did the calculations correctly. Are you able to solve for the second part of C) ?

alecwilson · Answer

I'm sorry I cannot, can you show me the correct way to solve c? @pythagoras123

pythagoras123 · Answer

If the container's dimensions are doubled: 

It will have a diameter of 26 inches and a height of 70 inches. 

Across the cylinder we can fit 26/2.63 = 9.88 spheres. We round this down to 9 spheres.

From top to bottom of the container, we can fit 70/2.63 = 26.6 spheres. We round this down to 26 spheres. 

Total number of spheres = 26 x 9 = 234 spheres.

pythagoras123 · Answer

234 tennis balls, I mean.

alecwilson · Answer

how'd you get all this?