Question

Please help and please show your work

Answer 1

The volume of all 9 spheres is 301.6
`in^3`

Explanation:

Notice that three of the identical spheres fit perfectly along the 12 in side box, therefore we know that the diameter of each is 12 in/3 = 4 in.

Then the radius of each sphere must be 2 inches (half of the diameter). Now that we know the radius of each sphere, we use the formula for the volume of a sphere to find it:

`V=(4)/(3) \pi R^3\\V=(4)/(3) \pi (2\,in)^3\\V=(4)/(3) \pi\, 8\,\,in^3\\V=(32)/(3) \pi\,\,in^3`

Now, the total volume of all nine spheres is the product of 9 times the volume we just found:

`V_(all \,9)=9\,*(32)/(3) \pi\,\,in^3\\V_(all \,9)=96 \pi\,\,in^3\\V_(all \,9)\approx \,301.6\,\,in^3`