A man would use the formula Volume = (4PI *R *R *R)/3 then multiply that answer by the Density (pounds / cubic inch) to determine how much a 6 inch lead ball weighs. The Density of Lead is 0.409 per cubic inch.

I want you to rewrite this formula to answer this problem completely backwards. what is the diameter in inches of a 10 pound lead ball? think carefully... Only the formula is required.

Question

A man would use the formula  Volume = (4PI *R *R *R)/3  then multiply that answer by the Density (pounds / cubic inch) to determine how much a 6 inch lead ball weighs.  The Density of Lead is 0.409 per cubic inch.

I want you to rewrite this formula to answer this problem completely backwards.  what is the diameter in inches of a 10 pound lead ball? think carefully...  Only the formula is required.

anonymous · Answer

I can see what is going on here in the formula clearly,  You must determine the Volume in cubic inches first, then multiply it by the density to determine overall weight,  But for the life of me I cant reverse this process and get a right answer

anonymous · Answer

I am guessing the final answer should be around 3.5 to 4 inches or so of lead.  But how I am doing it gives me a final answer of less than  1 every time.

kropot72 · Answer

Let dl = density of lead in lb/cu.in
Volume of 10 lb lead ball =
$$\frac{10}{dl}cubicins$$
$$\frac{10}{dl}=\frac{4\times \pi r ^{3}}{3}$$
$$r ^{3}=\frac{10\times 3}{dl \times 4\times\pi}$$

anonymous · Answer

Testing the formula now.... And thanks for taking the time to look at it for me!

kropot72 · Answer

You're welcome :)
When you take the cube root of r^3 you will have r. Then multiply by 2 to find the diameter.

anonymous · Answer

YAY!

kropot72 · Answer

Well done!

anonymous · Answer

3.6010 inches Diameter of a 10 lb lead ball