SOLUTION: The volume of a right cone is 372𝜋 cubic inches and the slant height makes an angle of 60° with the base. Find the altitude. Please can anyone help me?

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Question 1194399: The volume of a right cone is 372𝜋 cubic inches and the slant height makes an angle of 60° with the base. Find the altitude. Please can anyone help me?
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
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The volume of a right cone is 372𝜋 cubic inches and the slant height makes an angle
of 60° with the base. Find the altitude. Please can anyone help me?
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Let h be the height of the cone.


Then the radius "r" of the cone is  r = h%2Fsqrt%283%29,  from the 30°-60°-90° triangle.


Next, the volume of this cone is

      V = %281%2F3%29%2Api%2Ar%5E2%2Ah = %281%2F3%29%2Api%2A%28h%2Fsqrt%283%29%29%5E2%2Ah = %281%2F3%29%2Api%2A%281%2F3%29%2Ah%5E3 = %281%2F9%29%2Api%2Ah%5E3.


It gives you this equation

      %281%2F9%29%2Api%2Ah%5E3 = 372%2Api,


from which you get

    h%5E3 = 372*9 = 3348,

    h = root%283%2C3348%29 = 14.96 inches   (rounded).    ANSWER

Solved.


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Comment/question from student:  Ma'am can I ask?  What if the slant height makes an angle of 45°,  what would be the radius ma'am?



My response :   In this case,  r = h.


            It is  ELEMENTARY  KNOWLEDGE,  which is  PRE-requisite for solving such problems,

            and it is assumed that  EVERY  student  KNOWS  it as good as he  (or she)  knows the multiplication table.