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3 years ago

14

The height of a conical sand pile is always twice the radius. if sand is being added to the pile at a rate of 30π cubic centimet

ers per minute, how fast is the height of the pile increasing when the circumference of the base of the sand pile is 120π centimeters?

1 answer:

saw5 [17]3 years ago

4 0

Check the attached file for the answer.

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If the diameter of the cone is 5, then the radius of it will be half that, or 2.5, thus

$\bf \textit{total surface area of a cone}\\\\
SA=\pi r\stackrel{slant~height}{\sqrt{r^2+h^2}}+\pi r^2~~
\begin{cases}
r=radius\\
h=height\\
------\\
SA=43.75\pi \\
r=2.5
\end{cases}
\\\\\\
43.75\pi =\pi (2.5)\sqrt{r^2+h^2}+\pi (2.5)^2
\\\\\\
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\\\\\\
43.75\pi -6.25\pi =2.5\pi \sqrt{r^2+h^2}\implies 37.5\pi =2.5\pi \sqrt{r^2+h^2}
\\\\\\
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