What is the volume equation for a sphere?
The formula for the volume of a sphere is V = 4/3 πr³. See the formula used in an example where we are given the diameter of the sphere.
How are the rates of change of the radius and the volume related?
The rate of change of the radius dr/dt = . 75 in/min because the radius is increasing with respect to time. hence, the volume is increasing at a rate of 75π cu in/min when the radius has a length of 5 inches.
What is the area of the sphere?
Surface Area of Sphere = 4πr², where r is the radius of sphere. A sphere is a solid figure bounded by a curved surface such that every point on the surface is the same distance from the centre.
Why is the formula for surface area of a sphere?
The surface area of the sphere gets one-fourth when the radius is halved as r = r/2. As, surface area of sphere = 4πr2 = 4π(r/2)2 = πr2 = surface area/4. Thus, the surface area of the sphere gets one-fourth as soon as its radius gets halved.
Why is sphere volume formula?
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 sphere is a three-dimensional shape which is the reason that we can measure Volume and area of a Sphere.
How do you convert radius to volume?
The formula to determine the volume of a sphere is 4/3π multiplied by r, the radius, cubed, where π, or pi, is a nonterminating and nonrepeating mathematical constant commonly rounded off to 3.1416. Since we know the volume, we can plug in the other numbers to solve for the radius, r. Multiply the volume by 3.
How do we calculate change in volume?
The change in volume ΔV is very nearly ΔV = 3αVΔT. This equation is usually written as ΔV = βVΔT, where β is the coefficient of volume expansion and β ≈ 3α.
What is rate of volume?
In physics and engineering, in particular fluid dynamics, the volumetric flow rate (also known as volume flow rate, rate of fluid flow, or volume velocity) is the volume of fluid which passes per unit time; usually it is represented by the symbol Q (sometimes V̇). The SI unit is cubic metres per second (m3/s).