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Eight balls are in a box 18 inches long ,9 inches wide ,and 4.5 inches deep.if each ball has a diameter of 4.5 inches what is the volume of the space around the balls

Respuesta :

Answer:

I would say the answer would be 5382

Step-by-step explanation:

What i did was multiply 18 x 9 x 4.5 which would make 729 and if you multiply that by 8, you would get 5,382

yersanabria

Answer:

The volume of the space around the balls is:

  • 347.3 cubic inches.

Step-by-step explanation:

To calculate the result you must:

  1. Calculate the volume of the box.
  2. Calculate the summed volume of all the balls.

To calculate the volume of a box you must apply the following formula:

  • Volume of a box = Length * width * depth.

Therefore you must replace with the provided values:

  • Volume of a box = 18 inch * 9 inch * 4.5 inch
  • Volume of a box = 729 inch^3

Now the formula to calculate the volume of a sphere is:

  • Volume of a sphere = 4/3 PI * r^3

Remember that r (radius) is half the diameter, therefore the radius in this case is 2.25 inches, knowing this is replaced:

  • Volume of a sphere = 4 / 3PI * r^3
  • Volume of a sphere = 4 / 3PI * (2.25)^3
  • Volume of a sphere = 47.71 inch^3

But since there are 8 spheres, the value obtained must be multiplied by 8:

  • Volume of all spheres = 47.71 inch^3 * 8 = 381.7 inch^3

And we proceed to subtract the volume of the balls from the volume of the box:

  • Volume of space around = 729 inch^3 - 381.7 inch^3 = 347.3 inch^3