1. The first step to answering this question is to find the volume of a single spherical lead shot and then multiply this by 5000 to find the total volume of 5000 lead shots.
So, given that the lead shots are spherical, we must use the formula for the volume of a sphere:
V = (4/3)πr^3
Given that the diameter is 3mm, we can find the radius by dividing this by 2:
r = 3/2 = 1.5 mm
From here, there are two ways to proceed; we can either covert the radius into cm, or we can continue with the mm value and then convert the resulting volume in cubic mm into cubic cm (since we are given that 1 cm cubed of lead weighs 11.4g, we can already tell that we will have to finish with a volume in cubic cm). I will show both these methods as a) and b), respectively.
a) If there are 10 mm in 1 cm, and we have a radius of 1.5 mm, then to convert this into cm we need to simply divide by 10:
1.5 mm = 1.5/10 = 0.15 cm
Now that we have our radius in cm form, we can substitute this into the formula for the volume of a sphere that we specified at the very beginning:
V = (4/3)πr^3
V = (4/3)π(0.15)^3
V = (9/2000)π cm cubed, or
0.0045π cm cubed (in decimal form)
Now that we have the volume of one lead shot, all we need to do is multiply this by 5000 to find the volume of 5000 lead shots:
0.0045π*5000 = 22.5π cm cubed
Since we already have the total volume in cm cubed, there is no need to do any more conversions.
b) In this method, we will use radius = 1.5 mm and substitute this into the general formula for the volume of a sphere again:
V = (4/3)πr^3
V = (4/3)π(1.5)^3
V = (9/2)π mm cubed, or
4.5π mm cubed (in decimal form)
Thus, to calculate the volume of 5000 lead shots, we must multiply this value by 5000:
4.5π*5000 = 22500π mm cubed
Now comes the part where we must convert this into cubic cm; to do this we simply take the value in cubic mm and divide it by 10^3 (ie. 1000). Thus:
22500π/1000 = 22.5π cm cubed
As you can see, we end up with the same answer as in a). The key here is to remember that you need to convert, so maybe write a note to yourself at the start of the question and pay close attention to the different units in both the question and your working.
2. Now that we know that the volume of 5000 spherical lead shots is 22.5π cm cubed, we need to calculate their mass.
We are given that 1 cm cubed of lead weighs 11.4 g, thus to calculate the mass of 22.5π cm cubed of lead, we need to multiply this value by 11.4. Thus:
Mass = 22.5π*11.4
= 256.5π g
Note that this is the answer in exact form. I wasn't entirely sure about the rounding required or the value of π that you were specified to use (eg. exact, 22/7, 3.14), so if you wanted me to edit the answer to reflect that or had any questions, feel free to comment below.
