Answer:
The volume of the space around the balls is:
- <u>347.3 cubic inches</u>.
Step-by-step explanation:
To calculate the result you must:
- Calculate the volume of the box.
- 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:
- <u>Volume of space around = 729 inch^3 - 381.7 inch^3 = 347.3 inch^3</u>
