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What is the ratio of surface area to volume for a sphere with the following measurements?

Surface area = [tex]\(300 \, \text{m}^2\)[/tex]
Volume = [tex]\(500 \, \text{m}^3\)[/tex]

A. [tex]\(1.7 \, \text{m}^{-1}\)[/tex]
B. [tex]\(0.6 \, \text{m}^{-1}\)[/tex]
C. [tex]\(300 \, \text{m}^{-1}\)[/tex]
D. [tex]\(500 \, \text{m}^{-1}\)[/tex]


Sagot :

To find the ratio of the surface area to the volume for a sphere, you need to divide the given surface area by the given volume.

Here are the given values:
- Surface area [tex]\( = 300 \, \text{m}^2 \)[/tex]
- Volume [tex]\( = 500 \, \text{m}^3 \)[/tex]

We need to calculate the ratio of the surface area to the volume:
[tex]\[ \text{Ratio} = \frac{\text{Surface Area}}{\text{Volume}} \][/tex]

Substitute the given values into the formula:
[tex]\[ \text{Ratio} = \frac{300 \, \text{m}^2}{500 \, \text{m}^3} \][/tex]

Now, perform the division:
[tex]\[ \text{Ratio} = 0.6 \, \text{m}^{-1} \][/tex]

Therefore, the ratio of surface area to volume for the sphere is [tex]\( 0.6 \, \text{m}^{-1} \)[/tex], and the correct answer is:

B. [tex]\( 0.6 \, \text{m}^{-1} \)[/tex]
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