How is the surface area of a sphere related to its volume?

For a sphere, surface area is S= 4*Pi*R*R, where R is the radius of the sphere and Pi is 3.1415… The volume of a sphere is V= 4*Pi*R*R*R/3. So for a sphere, the ratio of surface area to volume is given by: S/V = 3/R.

How do you find the height of a sphere if you know the volume?

Volume of a spherical cap = (1/3)πh2(3R – h), where, height h of the spherical cap, and radius R of the sphere from which cap was cut. Volume of a spherical sector = (2/3)πR2h, where, R is radius of sphere, h is height.

How do you find the ratio of surface area to volume of a sphere of unit radius?

= 3 / r. 3 : r is the ratio of the surface area and the volume of the sphere of unit length.

Is the derivative of the volume of a sphere equal to its surface area?

The rate of change of the volume of the sphere is equal to the surface area of the sphere. The outside of the paint is the new boundary of the sphere, and the inside of the paint is added to the volume. This explains why the derivative (rate of change) of the volume is the surface area (SA).

Is surface area equal to volume?

Surface area is a two-dimensional measure, while volume is a three-dimensional measure. Two figures can have the same volume but different surface areas. For example: A rectangular prism with side lengths of 1 cm, 2 cm, and 2 cm has a volume of 4 cu cm and a surface area of 16 sq cm.

How the volume of sphere is derived?

The formula for calculating the volume of a sphere with radius ‘r’ is given by the formula volume of sphere = (4/3)πr3.

How do you find the ratio of a sphere?

So for a sphere, the ratio of surface area to volume is given by: S/V = 3/R.

How is volume of a sphere derived?

The volume of sphere is the amount of air that a sphere can be held inside it. The formula for calculating the volume of a sphere with radius ‘r’ is given by the formula volume of sphere = (4/3)πr3.

Is the surface area of a sphere greater than the volume?

The increase in volume is always greater than the increase in surface area. This is true for cubes, spheres, or any other object whose size is increased without changing its shape.

What is the volume of a sphere equal to?

The volume of a sphere is equal to the surface area of the sphere. If this value is equal to Nπ, what is the value of N? – Quora The volume of a sphere is equal to the surface area of the sphere.

How do you find the surface area of a sphere?

The formula for the surface area of a sphere is S = 4πr², and we are given in this case that 4πr² = Nπ. We now need to find the radius r of a sphere in which both the volume and the surface area of the sphere are numerically equal.

How do you find the volume of a hemisphere?

When a plane cuts the sphere in two equal halves, we get a hemisphere. The total surface area (TSA) of hemisphere is equal to the sum of its curved surface area and base area (circular base). Therefore, TSA (hemisphere) = Half of area of sphere + Base area TSA = 2πr² + πr². TSA = 3πr². Volume of Sphere

What is the equation to find radius are of a sphere?

Since it’s given for a sphere that its volume V and its surface area S are numerically equal, and since by an axiom that two things (in this case, V and S) that are equal to the same thing (in this case, Nπ) are equal to each other, then we can write the following equation to solve for radius r: V = S.