Find the volume of a smaller wedge cut from a sphere of radius 66 by two planes that intersect along a diameter at an angle of π
/6
1 answer:
Answer:
The answer is "
".
Step-by-step explanation:
please find the complete question in the attached file.
Let the sphere center be (0,0,0) and then let the intersection diameter lie all along the z-axis.
So one of the collision plans is the xz-plane the other is the path via an xz-plane angle.

All appropriate region could then be indicated in spherical coordinates

Calculating the volume:
![=\int_{0}^{\frac{\pi}{6}} \int_{0}^{\pi} \int_{0}^{a} \rho^2 \sin \phi d \rho d \phi d \theta\\\\ =\int_{0}^{\frac{\pi}{6}} d \theta \int_{0}^{\pi} \sin \phi d \int_{0}^{a} \rho^2 d \rho\\\\= [\theta]^{\frac{\pi}{6}}_{0} [-\cos \phi]^{\pi}_{0} [\frac{\rho^3}{3}]^{a}_{0}\\\\= \frac{\pi}{6} [1+1] \frac{a^3}{3}\\\\=\frac{\pi a^3}{9}](https://tex.z-dn.net/?f=%3D%5Cint_%7B0%7D%5E%7B%5Cfrac%7B%5Cpi%7D%7B6%7D%7D%20%5Cint_%7B0%7D%5E%7B%5Cpi%7D%20%5Cint_%7B0%7D%5E%7Ba%7D%20%5Crho%5E2%20%5Csin%20%5Cphi%20d%20%5Crho%20d%20%5Cphi%20d%20%5Ctheta%5C%5C%5C%5C%20%3D%5Cint_%7B0%7D%5E%7B%5Cfrac%7B%5Cpi%7D%7B6%7D%7D%20d%20%5Ctheta%20%5Cint_%7B0%7D%5E%7B%5Cpi%7D%20%5Csin%20%5Cphi%20d%20%5Cint_%7B0%7D%5E%7Ba%7D%20%5Crho%5E2%20d%20%5Crho%5C%5C%5C%5C%3D%20%5B%5Ctheta%5D%5E%7B%5Cfrac%7B%5Cpi%7D%7B6%7D%7D_%7B0%7D%20%5B-%5Ccos%20%5Cphi%5D%5E%7B%5Cpi%7D_%7B0%7D%20%5B%5Cfrac%7B%5Crho%5E3%7D%7B3%7D%5D%5E%7Ba%7D_%7B0%7D%5C%5C%5C%5C%3D%20%5Cfrac%7B%5Cpi%7D%7B6%7D%20%5B1%2B1%5D%20%5Cfrac%7Ba%5E3%7D%7B3%7D%5C%5C%5C%5C%3D%5Cfrac%7B%5Cpi%20a%5E3%7D%7B9%7D)
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Segment OX will be the radius.
YZ will be the tangent.
PQ might be the secant.
Hope this helps :)
X -3y = -15
Subtract 'x' from each side:
-3y = -x - 15
Divide each side by -3 :
<em>y = 1/3 x + 5</em>
This is 'slope-intercept' form.
Least value is too vague.
You can have least positive then answer is A.
You can have most negative then C.
Hope this helps.
Do what the hint says lol
answer is option D
because you can divide them like

so the option is D
please mark this answer as brainlist