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?
~~~~~~~~~~~~~~~~~~


<pre>
Let h be the height of the cone.


Then the radius "r" of the cone is  r = {{{h/sqrt(3)}}},  from the 30°-60°-90° triangle.


Next, the volume of this cone is

      V = {{{(1/3)*pi*r^2*h}}} = {{{(1/3)*pi*(h/sqrt(3))^2*h}}} = {{{(1/3)*pi*(1/3)*h^3}}} = {{{(1/9)*pi*h^3}}}.


It gives you this equation

      {{{(1/9)*pi*h^3}}} = {{{372*pi}}},


from which you get

    {{{h^3}}} = 372*9 = 3348,

    h = {{{root(3,3348)}}} = 14.96 inches   (rounded).    <U>ANSWER</U>
</pre>

Solved.



===============



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




<U>My response</U> :  &nbsp;&nbsp;In this case, &nbsp;r = h.



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


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