posted by Tho on .
The size to which a pumpkin grows while on the vine is probably problematic, as our current visiting POLY pumpkins demonstrate.
What if we were watching a pumpkin on the vine grow over time and that its shape was totally spherical.
Now for your five (5) tasks:
1. Initially we see a pumpkin when its radius equals 2”. Calculate its volume and surface area at this point.
2. Determine what the volume and surface area of the pumpkin will be when its radius equals 4”.
3. Determine what the radius of the pumpkin would have been when its volume was 2 times its initial volume.
4. Determine what the radius would have been when the pumpkin had a surface area 4 times the surface area it had when its radius was 4”.
5. Consider the volume of our pumpkin when its radius was 3”. What if there were a cylindrically-shaped pumpkin having that exact same volume. Determine 3 different radius and height combinations for the cylinder pumpkin that would generate that same volume. By the way, all 6 numbers must be different and must be integers.
v = 4/3 pi r^3
a = 4 pi r^2
plug in r=2
plug in r=4
or, just multiply the volume by 8 and the area by 4
multiply r by ∛2
if area is 4x, radius is 2x
v(3) = 4/3 pi * 27 = 36pi
just come up with values for r and h such that r^2 and h are factors of 36 since cylinder volume
v = pi r^2 h