What is the derivative of the area of a sphere?
The derivative of that is 4πr2 which represents the sphere’s surface area.
What is the equation for finding the area of a sphere?
A = 2 * π * r * 2 * r , A = 4 * π * r² , which is well-known area of a sphere formula.
What is dA of a sphere?
where dA is an area element taken on the surface of a sphere of radius, r, centered at the origin. The volume element is spherical coordinates is: d V = r 2 sin θ d r d θ d φ .
Why is surface area of sphere?
The Greek mathematician Archimedes discovered that the surface area of a sphere is the same as the lateral surface area of a cylinder having the same radius as the sphere and a height the length of the diameter of the sphere. The lateral surface area of the cylinder is 2πrh where h=2r .
Is dV Dr the area?
For a sphere, increasing the radius by dr, you add a uniform “coat of paint” to the volume, increasing it by dV = S dr. (Volume is “base area” times thickness, if we ignore the curvature.)
How do you find dV dt of a sphere?
Volume(V) of a sphere of radius r is calculated by 4pr^3 /3 and surface area(A) by 4pr^2. = 2/r × 4pr^2 × dr/dt = 2/r × dV/dt = 2/4×6 cm^2/s =3 cm^2/s.
Which equation is true?
To make a true equation, check your math to make sure that the values on each side of the equals sign are the same. Ensure that the numerical values on both sides of the “=” sign are the same to make a true equation. For example, 9 = 9 is a true equation. 5 + 4 = 9 is a true equation.
What is the value of a function?
The value of a function, given the value(s) assigned to its argument(s), is the quantity assumed by the function for these argument values.
How to calculate the surface area of a sphere?
The formula to calculate the volume of a sphere is given by the equation: Where r is the radius of the sphere. The formula to calculate the surface area of the sphere is given by: The Surface area of the sphere= square units.
When is P on the sphere with radius r?
P is on the sphere with radius r only when the distance from O to P is r. Since OAB is a right angle triangle, x 2 + y 2 = s 2. The triangle OBP is another right triangle and therefore, s 2 + z 2 = r 2.
Which is the general equation of a sphere?
which is called the equation of a sphere. If (a, b, c) is the centre of the sphere, r represents the radius, and x, y, and z are the coordinates of the points on the surface of the sphere, then the general equation of a sphere is (x – a)² + (y – b)² + (z – c)² = r² The formula to calculate the volume of a sphere is given by the equation:
When to use Pythagoras theorem for equation of sphere?
x 2 + y 2 = r 2 Pythagoras theorem can be used twice for the equation of a sphere. In the below figure, O is the origin and P (x,y,z) is a point in three-space. P is on the sphere with radius r only when the distance from O to P is r.