Question

The volume of a right cone is 6757 units. If its circumference measures 187 units,

find its height.

Answer 1

Answer: H≈7.3 units

Explanation:

`\displaystyle\\V_(cone)=(1)/(3)S_(circum)*H \\`

Multiply both parts of the equation by 3:

`\displaystyle\\V_(cone)(3)=(1)/(3) S_(circum)*H(3)\\\\3V_(cone)=S_(circum)*H\\\\Divide\ both\ parts\ of\ the\ equation\ by\ S_(circum) :\\\\H=(3V_(cone))/(S_(circum)) \\\\ Length\ circumference \ L=2\pi R\\Hence, divide\ both\ parts\ of\ the \ equation\ by\ 2\pi :\\\\R=(L)/(2\pi ) \\\\R^2=((L)/(2\pi ))^2\\\\R^2=(L^2)/((2\pi )^2) \\\\R^2=(L^2)/(4\pi ^2)\\\\S_(circum)=\pi R^2 \\\\S_(circum)=(\pi L^2 )/(4\pi ^2)\\\\ S_(circum)=(L^2)/(4\pi ) \\\\`

`\displaystyle\\Hence, \ \\\\H=(3v_(cobe))/((L^2)/(4\pi ) ) \\\\H=(3V_(cobe)*4\pi )/(L^2)\\\\H=(12\pi V_(cobe))/(L^2) \\\\V_(cobe)=6757\ units^3\ \ \ \ \L=187\ units\\\\Hence,\\\\H=(12\pi*6757 )/(187^2) \\\\H\approx7.3\ units`