contraurerfje

2023-03-24

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

Bollacasaep22

Beginner2023-03-25Added 6 answers

Surface area of a sphere with radius $r$ equals to $4\pi {r}^{2}$

The volume of this sphere is $\frac{4}{3}\pi {r}^{3}$

Consequently, the surface area to volume ratio is equal to

$\frac{4\pi {r}^{2}}{\frac{4}{3}\pi {r}^{3}}=4\left(\frac{3}{4}\right)\left(\frac{\pi}{\pi}\right)\left(\frac{{r}^{2}}{{r}^{3}}\right)=\frac{3}{r}$

The volume of this sphere is $\frac{4}{3}\pi {r}^{3}$

Consequently, the surface area to volume ratio is equal to

$\frac{4\pi {r}^{2}}{\frac{4}{3}\pi {r}^{3}}=4\left(\frac{3}{4}\right)\left(\frac{\pi}{\pi}\right)\left(\frac{{r}^{2}}{{r}^{3}}\right)=\frac{3}{r}$

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