Suppose a certain cylinder has a volume of 6433.98...

Question

Suppose a certain cylinder has a volume of 6433.98175 cm3.

Questions:

What are 5 different combinations of radius and height that will lead to this volume?
What are the surface areas of these cylinders that you came up with for Number 1?
Are there any cylinders that you came up with that have the same surface area? Why do you think this is?

Answer 1

Volume = (Area of the base)(Height) = (pi)*r²*h

 

Where pi=3.14159, r = the cylinder's radius, and h = its height.  So, for your problem:

 

(pi*r²*h) = 6433.98175

r²*h = (6433.98175)/(pi)        [Divided both sides by pi]

r²*h = 2048

 

h = 2048/r²

 

Pick a value of r, then use the above equation to determine the value of h that will give a volume of 6433.98175 cm³.  For example, for r = 10 cm

 

h = 2048/10² = 2048/100 = 20.48 cm

 

So the combination is r = 10 cm, h = 20.48 cm.  Check:

 

Volume = (pi)*(10²)(20.48) = (3.14159)(100)(20.48) = 6433.98175

 

The formula for the cylinder's surface area is:

 

Surface Area = 2(pi)r² + 2(pi)rh = 2(pi)r(r+h)

 

Use this formula to compute the surface areas for your selected values of r and h.  For the combination r=10, h=20.48

 

Surface Area = 2(3.14159)(10)(10+20.48) = 1915.11 cm²