Simple math question?

Question

well, i am taking AP-calculus this year and now i am on the application of minimum and maximum. the stupid thing i cant understand is the (volume) and the (surface area) , i dont know what is the difference between them

I.E: the volume of a rectangular solid .....

Answer 1

Q. Simple math question?

A. Application of minimum and maximum


Do you mean Minima and Maxima? Because that is the mathematically correct term in Calculus? Anyways, your question is about the difference between volume and surface area.

Volume = capacity of a solid object i.e. the total space it has INSIDE it

Surface Area = Total area of material used to construct the solid object. Imagine yourself making a cone out of wood. By surface area, you're interested in knowing how many square inches of wood have to be cut to make the solid cone.

In case of rectangular solid of length L, breadth B and height H,

Volume = L x B x H

Surface Area = 2 x (LxB + LxH + BxH)

In case of a cube, L = B = H = any damn variable X

So Volume = X x X x X = X^3

Surface Area = 6 x X^2

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Answer 2

A good way to understand difference between surface and volume in a space of an arbitrary dimension is that the surface is the "skin" of an object, the volume is his inside content.

For a sphere, the volume is 4/3*pi*R^3 and the surface is 4*Pi*R^2 where R is the radius of the sphere. It illustrates that the volume is of same dimension as the space (R^3 for dimension 3) and the surface of one less dimension (R^2 for dimension 2). It also illustrates that differentiate the volume in the case of the sphere give the surface.

Answer 3

Think of a brick. The volume is the space taken up by the brick. The surface area is the amount of covering it would take to paper the whole brick. Volume tells about the inside while surface area tells about the outside.

Answer 4

The volume of a rectangular solid is length X width X height cubic units.

The surface area is 2(lw +lh + wh) and is measured in square units. Think of the surface area of a solid as the the nubber of square units you would have to cover the outer surface with paint.

Answer 5

Volume is 3-dimensional, surface area is 2-dimensional. For a rectangle you'd need length, width, and height for volume, and only length and width for surface area.

In terms of calculus, think of surface area as a layer of what's on the outside, and volume as counting what you can fill on the inside.

Answer 6

volume is whats inside the object while surface area is the area of each side of the shape thingie added together both can be 3d