Question #f9702

1 Answer
Oct 11, 2015

Tom - draw a sketch of the problem and label the lengths of the sides, then use the formula for the volume of a cone.

Explanation:

Here is a sketch of the triangle:

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Volume Cone = 1/3pir^2h13πr2h

Let's revolve around x which will make xx the height of the cone. The radius will be sqrt(10^2-x^2)102x2

Substitute these values into the formula for Volume:

Volume =1/3pi[sqrt(10^2-x^2)]^2*x=1/3pi(100x-x^3)Volume=13π[102x2]2x=13π(100xx3)

Since this course does not use calculus yet, graph the function:

y = 1/3pi(100x-x^3)y=13π(100xx3) between x= 0 and x=10, then use your graphing calculator to find the value for x that will maximize the volume :

x~~5.7735x5.7735 [Volume~~403][Volume403]

Hope that helped