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Yes. To prove this, consider a simple example -- a cube. The volume of a cube is s3 where s is the length of one edge of the cube. The surface area is equal to 6s2 still using s as the length of one edge of the cube. So now we just need to solve the equation: 6s2 = s3 To do that simply divide each side by s2. Now we have 6 = s. So a cube with an edge of length six units will have an equal volume and surface area. To double check, the volume is 63 = 216. The surface area is 6 x 62 = 63 = 216. Note that although the values are the same (216) the units of measurement are still different: units2 for the surface area and units3 for the volume.
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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.
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.
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.
Is it possible to have the same surface area different volume?
yes.
How are volume and surface area the same when volume stays the same?
There is no reason for the surface area to remain the same even if the volume is the same.
Do figures with the same volume always have the same surface area?
figures with the same volume does not have the same surface area.
Is it possible for 2 cubes to have the same volume and the same surface area?
Yes they would have to be similar cubes.
How is it possible for objects to have the same volume but different area?
Yes. A cube that is 2x2x2 has the same volume as a rectangular prism that is 1x2x4, which is 8. The surface area of the cube is 24 while the surface area of the rectangular prism is 28.
Do cubes have the same volume and surface area?
Yes Volume: Is the amount it takes to build it. Surface Area: Is how much is on the surface.
Can two rectangular prisms have the same surface area but different volume?
Yes, they can. They can also have the same surface area, but different volume.
How are volume and surface area the same?
Volume and surface area can never be the same because volume is a measure in 3-dimensional space whereas area is a measure in 2-dimensional space. The dimensions are different and so equality is not possible.Volume and surface area can never be the same because volume is a measure in 3-dimensional space whereas area is a measure in 2-dimensional space. The dimensions are different and so equality is not possible.Volume and surface area can never be the same because volume is a measure in 3-dimensional space whereas area is a measure in 2-dimensional space. The dimensions are different and so equality is not possible.Volume and surface area can never be the same because volume is a measure in 3-dimensional space whereas area is a measure in 2-dimensional space. The dimensions are different and so equality is not possible.
What is the ratio of surface area to volume for a sphere with surface area and volume m?
If they have the same radius then it is: 3 to 2
Is the volume of a cylinder the same as the surface area of a cylinder?
no
As a cell becomes larger what happens to its surface area and volume?
The Volume increases faster than the Surface Area
How does the surface area to volume ratio change as the cell size increases?
It decreases. As the dimensions increase by a number, the surface area increases by the same number to the power of 2, but the volume increases by the same number to the power of 3, meaning that the volume increases faster than the surface area.
