Surface area, as you know, is a planar measurement, and is measured in square units. Volume, on the other hand, is a solid measurement and is measured in cubic units. Both measures are necessary to understand a solid figure. For angular figures, such as prisms and pyramids, the area and volume calculations are straightforward, utilizing your knowledge of triangles and quadrilaterals. When you introduce curvature, as in a sphere, the calculations are not as intuitive?you will likely need to memorize the formulas. Is the ratio of surface area to volume of a sphere a constant, or does it vary with radius? How would you figure it? Which would cool faster in outer space?a large planet or a small planet? Why
2007-01-04 07:09:45 · 7 answers · asked by sol 1 in Science & Mathematics ➔ Mathematics
The ratio of surface area to volume varies with radius.
Area = 4*pi*r^2 and volume = 4/3*pi*r^3 so the ratio is 4*pi*r^2/(4/3)*pi*r^3 which equals 3/r and you see the ratio falls as the sphere increases in size.
A small planet cools faster than a large planet, at least as concerns radiative cooling (and assuming similar construction and starting temperature to drive the cooling) since the ratio of the surface area through which the cooling occurs is much higher for a much smaller planet so more of the small planet radiates directly out rather than outward... into itself, not quite into space.
Three sentences. Good way to avoid my longer winded answers! Hope the limited explanations help you.
2007-01-04 07:32:56 · answer #1 · answered by roynburton 5 · 1⤊ 0⤋
V = 4/3 *pi*r^3
A = 4*pi*r^2
So the ratio of A:V would always be 4*pi*r^2 : 4/3 *pi*r^3 or 3:r. Therefore the ratio is dependent on the radius. So as r increases the volume increases at a faster rate since r^3 increases faster than r^2. This means that a small planet would cool faster than a large one since the surface area is larger in proportion to its volume.
2007-01-04 07:13:12 · answer #2 · answered by E 5 · 0⤊ 0⤋
The surface area of a sphere increases proportionally to the square of the radius while the volume increases proportionally to the cube of the radius. So, the volume increases faster than the surface area.
Hope this helps.
2007-01-04 07:14:45 · answer #3 · answered by hcbiochem 7 · 0⤊ 0⤋
Ratio: s/v= 4*PI^2/(4/3*PI*r^3)=3/r
So it varies with radius.
Small planet would cool faster, as cooling is directly linked to surface area and internal energy is linked to mass which is proportional to volume.
2007-01-04 07:20:34 · answer #4 · answered by TfC_137 3 · 0⤊ 0⤋
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2016-05-23 03:17:06 · answer #5 · answered by Barbara 4 · 0⤊ 0⤋
Three sentences? How about:
1. I don't know
2. I don't care
3. Why are you asking me?
2007-01-04 07:13:12 · answer #6 · answered by Larry H 3 · 1⤊ 1⤋
What ever?
2007-01-04 07:16:55 · answer #7 · answered by Anonymous · 1⤊ 1⤋