Question

the senior class has decided to prank the math department. they plan to fill the math longe with golf balls. if the lounge has the following measurements: 10 feet high, 25 feet wide, and 25 feet long. how many golf balls are needed to fill it, if the diameter of a golf ball is 1.68 inches?Volume of a sphere= 4/3 pi r^3Volume of room= L*H*W(round answer to the nearest whole number)( Hint: packing spheres in a rectangular prism usually takes up 190% of the volume of the spheres)number of golf balls= (volume of the room)/(packing space of spheres)

Answer 1

We know that

• The lounge is 10 feet high, 25 feet wide, and 25 feet long.

,

• The diameter of a golf ball is 1.68 inches.

First, we find the volume of a golf ball

`V=(4)/(3)\pi r^3`

Where pi=3.14, r=0.84.

`V=(4)/(3)\cdot3.14\cdot(0.84)^3=1.33\cdot3.14\cdot0.59=2.46in^3`

The volume of a golf ball is 2.46 cubic inches.

Now, we find the volume of the lounge.

`V_(lounge)=l\cdot h\cdot w=25\cdot10\cdot25=6,250ft^3`

The volume of the lounge is 6,250 cubic feet.

To know the total number of golf balls needed, we just have to divide

`n=(6,250)/(2.46)=2,540.7`

Therefore, we need 2,540 golf balls to fill the longe completely.