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) = \(\pi r^{2}h\)
Assume \(\pi\) = \(\frac{22}{7}\)
V = 9891 \(m^{3}\)
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 = \(\pi r^{2}h\)
: . 9891\(m^{3}\) = \(\frac{22}{7} * r^{2} * (56m)\)
Making r the subject of this equation:
\(r^{2} = \frac{V}{( \pi ) (h)}\)
\(r = \sqrt{ \frac{V}{ ( \pi ) (h)} }\)
Since the Diameter is 2r then multiply both sides of the equation by 2
: . \(2r = 2 (\sqrt{ \frac{V}{( \pi ) (h)} } )\)
thus D = \(2 (\sqrt{ \frac{V}{( \pi ) (h)} } )\)
Part B:
Since the formula for Diameter has be formulated, substitute the values of the variables and solve for D
D = \(2( \sqrt{ \frac{9891 m^{3} }{ (\frac{22}{7}) (56m) }\)
: . D = \(2( \sqrt{56.199 m^{2} })\)
= 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.
