0
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.
Still curious? Ask our experts.
Chat with our AI personalities
Blake
Ezra
RossAdd your answer:
Earn +20 pts
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.
