1. 1) Since the ball (sphere) is round and the box square (cube), the problem wants to know how
much space is left in the cube that is not being occupied by the sphere.
We calculate the volume of both and then deduct the volume of the sphere from that of the
cube.
Cube: 20 × 20 × 20 = 8,000cm^#
Sphere: 4/3 × pi × 10^3= 4/3 × 3.1416 × 1000 = 4,188.79cm^3  subtract this from 8,000 and
you have your answer
2) Calculate volume of the “ice cream cone”:
We first calculate the sphere, then take ½ since we are dealing with ½ of a sphere:
Same formula as above, using the radius. They’re giving us the diameter, so we can either do it
the way I’m going to do it or you can simply just take the value of ½ of 18 = 9, whatever’s easier
for you.:
4/3 × pi × (½ ×18)^3
4/3 x 3.1416 × 729 = 3053.64 we need half of this: 3053.64/2= 1526.82
Now the cone:
1/3 pi(r^2)h = 1/3 × 3.1416 × 81 × 12 = 1017.88  add this to the 1526.82 and you have your
answer
3) The cylinder has a volume of 400pi and a diameter of 20. How high is it. This is very easy.
Trivia: The formula for the volume of a cylinder is the same as the one for the cone except we
don’t multiply times 1/3. This is because a cone goes into a cylinder, but because of its shape it
only occupies 1/3 of the space of the cylinder.
So here we go:
V = pi(r^2)h, find h. First let’s isolate h. Note h is being multiplied by pi(r^2), so we’ll divide both
sides by pi(r^2):
V/ pi(r^2) = h
Now we can work the formula:
400/(3.1416 × 81) = h You do the math, I’m too tired to use the calculator ;‐)
Regards,
John