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What is the surface area to volume ratio of a sphere?

Answer
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Hint: This type of question depends on the concept of finding volume and surface area of a sphere. Here, we first find the volume and surface area of the sphere and then take the ratio. We know that the volume of a sphere is given by 4πr33 while formula for calculating surface area of a sphere is 4πr2 where r represents the radius of the sphere.

Complete step by step solution:
Now we have to find out the ratio of surface area to volume of a sphere.
We know that the surface area of a sphere with radius r is given by,
Surface Area = 4πr2
Also we know that the formula for the volume of a sphere is
Volume = 4πr33
Hence, we can write ratio of surface area to volume is equal to
Surface AreaVolume= (4πr2(4πr33))
Surface AreaVolume=(4πr243πr3)
We can simplify it further,
Surface AreaVolume=4×(34)×(ππ)×(r2r3)
Thus we can obtain the final ratio as
Surface AreaVolume=3r
Surface Area : Volume = 3:r

Hence the surface area to volume ratio of a sphere is 3:r

Note: In this type of problem students may make mistakes in writing formulas for surface area as well as volume of sphere. Also students have to take care in calculation of ratio as we have to find surface area to volume ratio so we must divide surface area by the volume of the sphere. In case of simplification also we have to separate out each and every term which will help us in cancellation of common terms easily.

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