Using the volume of the cone, it is found that:
Height and diameter are both 33.7 feet.
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The volume of a cone with height h and diameter d is given by:
[tex]V = \frac{\pi d^2h}{12} = \frac{3.1415 d^2h}{12}[/tex]
In this question:
[tex]10000 = \frac{3.1415h^3}{12}[/tex]
[tex]3.1415h^3 = 120000[/tex]
[tex]h^3 = \frac{120000}{3.1415}[/tex]
[tex]h^3 = 38197.19[/tex]
[tex]h = \sqrt[3]{38197.19}[/tex]
[tex]h = 33.7[/tex]
Thus, both are 33.7 feet.
A similar problem is given at https://brainly.com/question/16717748