Question 1210269
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A cone and right pyramid have equal height and volumes. 
If the area of the base of pyramid is 154cm square, find the base radius of the cone
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<pre>
Let h be the common height.

The volume of the pyramid is  {{{(1/3)*154*h}}}.

The volume of the cone is  {{{(1/3)*pi*r^2*h}}}.


Equate the volumes  {{{(1/3)*154*h}}} = {{{(1/3)*pi*r^2*h}}}.


Cancel  {{{(1/3)*h}}}  in both sides.  You will get

    {{{pi*r^2}}} = 154

    {{{r^2}}} = {{{154/3.14159265}}} = 49.02  (rounded)

    r = {{{sqrt(49.02)}}} = 7.001.


<U>ANSWER</U>.  The radius of the cone is about 7 cm.
</pre>

Solved.