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Do figures with the same volume always have the same surface area?
figures with the same volume does not have the same surface area.
If two rectangular prisms have the same volume do they have the same surface area?
well, they can, but they dont have to be no. :)
Do solids that have the same volume have the same surface area?
Not necessarily. Having the same volume does not mean having the same surface area. As an example, if you were to take a sphere with volume 4/3*pi*r^3, and a suface area of 4*pi*r^2, and compare it to a cube with sides 4/3, pi, and 4^3, you would find that they had a different surface area, but the same volume. Let the radius of the sphere be 2, that is r = 2. In this case the surface are of the sphere is about 50, and the surface are of the cube is about 80. So a sphere and a cube, both with a volume of about 33.51 (4/3 * pi * 8), have different surface areas.
Is surface area the same as volume?
No. How can they be the same, if one of them is a two-dimensional measure, the other a three-dimensional measure.
What happens to the volume of an object as its surface area increases?
In general, the volume will also increase. If the shape remains the same, the volume will increase faster than the surface area. Specifically, the surface area is proportional to the square of an object's diameter (or any other linear measurement), while the volume is proportional to the cube of any linear measurement.
