The leaning tower of pisa is cylindrical and as such the volume can be approximated using the same formula as a regular cylinder.
Volume of a cylinder (V) = [tex] \pi r^{2}h [/tex]
Assume [tex] \pi [/tex] = [tex] \frac{22}{7} [/tex]
V = 9891 [tex] m^{3} [/tex]
h = 56 m
Let: Radius= r
Diameter= D
Then D= 2r
By substituting the known values into the equation and transposing one can formulate an equation to solve for D.
V = [tex] \pi r^{2}h [/tex]
: . 9891[tex] m^{3} [/tex] = [tex] \frac{22}{7} * r^{2} * (56m) [/tex]
Making r the subject of this equation:
[tex] r^{2} = \frac{V}{( \pi ) (h)} [/tex]
[tex]r = \sqrt{ \frac{V}{ ( \pi ) (h)} } [/tex]
Since the Diameter is 2r then multiply both sides of the equation by 2
: . [tex]2r = 2 (\sqrt{ \frac{V}{( \pi ) (h)} } )[/tex]
thus D = [tex]2 (\sqrt{ \frac{V}{( \pi ) (h)} } )[/tex]
Part B:
Since the formula for Diameter has be formulated, substitute the values of the variables and solve for D
D = [tex]2( \sqrt{ \frac{9891 m^{3} }{ (\frac{22}{7}) (56m) }[/tex]
: . D = [tex]2( \sqrt{56.199 m^{2} }) [/tex]
= 2 * 7.497m
= 14.993 m
Part C:
Therefore it can be concluded that the Diameter of the base of the Leaning Tower of Pisa is approximately 14.99 meters.
