Can someone help me with this?

Velannah

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Mar 21, 2019
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I would be very grateful if someone could help me with this task...?

Circular cone shaped Mount Fuji is 3776 meters high and the volume is 1400km^3 . What is the obliquity of the hillside?
 
Hello, and welcome to FMH! :)

The volume of a right circular cone is:

[MATH]V=\frac{1}{3}\pi r^2h[/MATH]
Can you solve this for \(r\)?
 
To follow up, we find:

[MATH]r=\sqrt{\frac{3V}{\pi h}}[/MATH]
And so the obliquity is:

[MATH]\theta=\arctan\left(\frac{h}{r}\right)=\arctan\left(h\sqrt{\frac{\pi h}{3V}}\right)[/MATH]
Plugging in the given data, and converting to degrees, we find:

[MATH]\theta\approx11.35^{\circ}[/MATH]
 
To follow up, we find:

[MATH]r=\sqrt{\frac{3V}{\pi h}}[/MATH]
And so the obliquity is:

[MATH]\theta=\arctan\left(\frac{h}{r}\right)=\arctan\left(h\sqrt{\frac{\pi h}{3V}}\right)[/MATH]
Plugging in the given data, and converting to degrees, we find:

[MATH]\theta\approx11.35^{\circ}[/MATH]
Thanks a lot!!
 
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