SOLUTION: three golf balls are sold in a square prism instead of a cylinder. Find the amount of empty space in the square prism if the golf balls all touch the sides, top and bottom of prism
Algebra ->
Volume
-> SOLUTION: three golf balls are sold in a square prism instead of a cylinder. Find the amount of empty space in the square prism if the golf balls all touch the sides, top and bottom of prism
Log On
Question 657047: three golf balls are sold in a square prism instead of a cylinder. Find the amount of empty space in the square prism if the golf balls all touch the sides, top and bottom of prism, and they have a diameter of 1.68 inches Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website! We want to calculate the volume of the three balls, and the volume of the box.
The amount of empty space will be the difference: the volume of the box minus the volume of the balls.
The volume of a box shaped prism is calculated by multiplying all three dimensions: width of the base, length of the base and height.
The width and length of the square base of the box will be the diameter of a ball: inches.
The height of the box will be three times that, inches = inches.
The volume of the box is cubic inches = cubic inches (rounded to two decimal places).
The volume, of a sphere of radius can be calculated using the formula
The radius is half of the diameter, so the radius of a ball would be
You will have to round the value of in your calculations,
As you multiply to get and the volume, you will end with way too many digits, so you will want to round again.
Using (rounded), the volume of one ball is cubic inches (rounding at each step of the calculation)
The volume of all 3 balls would be cubic inches = cubic inches.
The difference is the amount of empty space in the box: cubic inches - cubic inches = cubic inches.
