What is the relation between volume and surface area?

The surface area to volume ratio of an object is the relationship between two measurements. It is the ratio of Surface area to volume. It shows the comparison between the size of the outside of an object and the amount inside. Small or thin objects have a large surface area compared to the volume.

Why is the derivative of volume equal to 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).

What is the relationship between the volume and surface area of the sphere shown?

As we know, the formula of volume of a sphere is (4/3)πr3, and the formula of the surface area of the sphere is 4πr2. Thus, the ratio of the surface area of a sphere to the volume of a sphere of unit radius is given as (4π)/(4/3)π = 3:1.

What is the relationship between surface area and volume of a cylinder?

A cylinder’s volume is π r² h, and its surface area is 2π r h + 2π r². Learn how to use these formulas to solve an example problem.

What is the second derivative of volume?

The second derivative can be used to determine the minimum surface area of a cylinder with a given volume. Recall that the volume of a cylinder is V=πr2h, where r is the radius of the base, and h is the height of the cylinder.

What is the derivative of volume of a cube?

Derivation for Volume of a Cube We know that a cube is a 3-dimensional object whose all the sides i.e. length, breadth, and height are equal. Now for a cube, the volume derivation will be as follows: Consider a square sheet of paper.

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.

What is the ratio of the volume of the sphere to the volume of the cylinder?

2/3
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 between the volume of a cylinder?

The formula for computing the volume of a cylinder is V = pi * r^2 * h where V = the volume; pi = a constant roughly equals to 3.1415926; r = the radius of the circular base; h = the height of the cylinder.