What is the equation of a sphere in 3D?

Sphere’s are the 3D representations of circles. The equation of a sphere is similar to that of a circle, but with an extra variable for the extra dimension. (x−h)2+(y−k)2+(z−l)2=r2 In this equation, r=radius. The coordinate (h,k,l) tells us where the center of the sphere is.

Why is the sphere formula 4 3?

Volume of a sphere = 4/3 πr3 If you consider a circle and a sphere, both are round. The difference between the two shapes is that a circle is a two-dimensional shape and a sphere is a three-dimensional shape which is the reason that we can measure the Volume and area of a Sphere.

How do you write the equation of a sphere in standard form?

Answer: The equation of a sphere in standard form is x2 + y2 + z2 = r2. Let us see how is it derived. Explanation: Let A (a, b, c) be a fixed point in the space, r be a positive real number and P (x, y, z ) be a moving point such that AP = r is a constant.

What is the parametric equation of a sphere?

These are parametric equations of a plane. x = sinφcosθ y = sinφsinθ z = cosφ. gives parametric equations for the unit sphere. x = r sinucosv y = r sinusinv z = r cosu 0 ≤ u ≤ π, 0 ≤ v ≤ 2π will give a sphere of radius r.

How do you convert an equation into spherical coordinates?

To convert a point from Cartesian coordinates to spherical coordinates, use equations ρ2=x2+y2+z2,tanθ=yx, and φ=arccos(z√x2+y2+z2). To convert a point from spherical coordinates to cylindrical coordinates, use equations r=ρsinφ,θ=θ, and z=ρcosφ.

What is the equation of the line through the origin and the centre of the sphere?

The Plane 6x + ky + 3z – 12 = 0 where k ≠ 0 meets the coordinate axes at A, B and C respectively. The equation of the sphere passing through the origin and A, B, C is x2 + y2 + z2 – 2x – 3y – 4z = 0.

Is a sphere 2/3 of a cylinder?

Note : The volume of a sphere is 2/3 of the volume of a cylinder with same radius, and height equal to the diameter.

What is the relationship of sphere and cylinder?

(Answer: The sphere takes up two-thirds of the volume of the cylinder.)

What is the center of the sphere?

A sphere is a three dimensional figure that is the set of all points equidistant from a fixed point, called the center. The diameter of a sphere is a line segment which passes through the center and whose endpoints lie on the sphere.