Question #f9702

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Question #f9702

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Answer 1 · 2015-10-11T00:25:34

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:

enter image source here

Volume Cone = $\frac{1}{3} π r^{2} h$ $1/3pir^2h$

Let's revolve around x which will make $x$ $x$ the height of the cone. The radius will be $\sqrt{10^{2} - x^{2}}$ $sqrt(10^2-x^2)$

Substitute these values into the formula for Volume:

$V o l u m e = \frac{1}{3} π {[\sqrt{10^{2} - x^{2}}]}^{2} \cdot x = \frac{1}{3} π (100 x - x^{3})$ $Volume =1/3pi[sqrt(10^2-x^2)]^2*x=1/3pi(100x-x^3)$

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

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

$x \approx 5.7735$ $x~~5.7735$ $[V o l u m e \approx 403]$ $[Volume~~403]$

Hope that helped

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