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How to show that the rate of change of the volume of a cube with respect to the length of its edges is equal to have the surface area of the cube?
If the length of an edge is x, the volume is x3
To find the rate of change of the volume with respect to x, differentiate: d(x3)/dx = 3x2 The area of one face is x2 There are six faces so the total surface area is 6x2 Therefore the rate of change of volume, 3x2 , is half of 6x2 , the surface area.
What else can I help you with?
How to Converting volume to surface area?
Volume=area * length of that surface
How does the surface area of a rectangular prism change when the length and width and height are doubled?
if length and width are doubled then the volume should mulitiply by 8
What are some rules for volume and surface area?
volume is length x base x height and surface area is volume divided by height~
What is Surface area and volume of cube formula?
For a cube with sides of length x, surface area = 6x2 and volume = x3.
If the length side of a cube is increased the surface areea to volume ratio of the cube?
When the side length of a cube is increased, the surface area increases at a different rate compared to the volume. The surface area of a cube is given by (6a^2) and the volume by (a^3), where (a) is the length of a side. As the side length increases, the surface area-to-volume ratio decreases, meaning that larger cubes have a lower ratio compared to smaller cubes. This reflects that while more surface area is created, the volume increases even more significantly.
How to Converting volume to surface area?
Volume=area * length of that surface
How does the surface area of a rectangular prism change when the length and width and height are doubled?
if length and width are doubled then the volume should mulitiply by 8
A cube has a volume of 729cm3 what is the length and surface area?
Length = 9cm and total surface area is 486cm2
What is the surface area volume of a cube that is 5mm in length?
The total surface area is 150mm2 and the volume of the cube 125mm3
What are some rules for volume and surface area?
volume is length x base x height and surface area is volume divided by height~
What is Surface area and volume of cube formula?
For a cube with sides of length x, surface area = 6x2 and volume = x3.
Is the question the amount of water in a lake length area surface area or volume?
Volume
A cardboard box has a length of 3 feet height of 2 feet and depth of 2 feet If the length and depth are doubled by what percent does the volume of the box change?
300% The volume of the original box is ?. The volume of the box with the length and depth doubled is ?. The amount of change in volume is 60 - 15 = 45. The percent change is the amount of change in volume divided by the original volume:
If the length side of a cube is increased the surface areea to volume ratio of the cube?
When the side length of a cube is increased, the surface area increases at a different rate compared to the volume. The surface area of a cube is given by (6a^2) and the volume by (a^3), where (a) is the length of a side. As the side length increases, the surface area-to-volume ratio decreases, meaning that larger cubes have a lower ratio compared to smaller cubes. This reflects that while more surface area is created, the volume increases even more significantly.
What is the characteristic length of a sphere and how does it affect the sphere's properties?
The characteristic length of a sphere is its diameter, which is the distance across the sphere passing through its center. The characteristic length affects the sphere's properties such as volume, surface area, and density. A larger characteristic length means a larger volume and surface area, while a smaller characteristic length means a smaller volume and surface area.
What is the unit for surface area to volume ratio?
1/length
How do you find the volume and surface area of a parellagram?
It has no volume because it's a 2D shape but its surface area is:- length*perpendicular height
