- #1
marutkpadhy
- 9
- 0
Find the radius of the circular section of the sphere of the sphere x^2 + y^2 + z^2 = 49 by the plane 2x+3y-z-5 \sqrt{14}= 0
Calculating Radius of Circular Section from Sphere and Plane Intersection
In summary, to find the radius of the circular section of the sphere x^2 + y^2 + z^2 = 49 by the plane 2x+3y-z-5 \sqrt{14}= 0, one can solve the equation of the plane for z, substitute it into the equation of the sphere, and then find the distance d from the center of the sphere to the plane. From there, the radius r of the circular section can be found using the formula for the distance from a point to a plane.
- #2
MarkFL
Gold Member
MHB
- 13,288
- 12
Suppose you solve the equation of the plane for $z$, and then substitute for $z$ into the equation of the sphere...what do you get?
- #3
Evgeny.Makarov
Gold Member
MHB
- 2,436
- 4
View attachment 2708
I think it is easier to find the distance $d$ from the center of the sphere to the plane (recall the the distance from $(x_0,y_0,z_0)$ to $Ax+By+Cz+D=0$ is $\dfrac{Ax_0+By_y+Cz_0+D}{\sqrt{A^2+B^2+C^2}}$) and then find the radius $r$ of the required circular section from the right triangle.
I think it is easier to find the distance $d$ from the center of the sphere to the plane (recall the the distance from $(x_0,y_0,z_0)$ to $Ax+By+Cz+D=0$ is $\dfrac{Ax_0+By_y+Cz_0+D}{\sqrt{A^2+B^2+C^2}}$) and then find the radius $r$ of the required circular section from the right triangle.
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Related to Calculating Radius of Circular Section from Sphere and Plane Intersection
What is the radius of a circular section?
The radius of a circular section is the distance from the center of the circle to its edge or circumference.
How is the radius of a circular section calculated?
The radius of a circular section can be calculated by dividing the diameter of the circle by 2, or by using the formula r = C/2π, where r is the radius and C is the circumference.
What is the significance of the radius of a circular section?
The radius of a circular section is an important measurement in geometry and is used to determine the size and proportions of circles and other curved shapes. It is also used in various mathematical calculations and equations.
Can the radius of a circular section be negative?
No, the radius of a circular section cannot be negative as it is a measurement of distance and distance cannot be negative.
How does the radius of a circular section affect the area and circumference of a circle?
The radius of a circular section is directly related to the area and circumference of a circle. As the radius increases, the area and circumference of the circle also increase proportionally. Similarly, as the radius decreases, the area and circumference decrease proportionally.
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