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(B) The surface area to volume ratio for a sphere is given by the formula: $\frac{SA}{V} = \frac{4 \pi r^2}{\frac{4}{3} \pi r^3} = \frac{3}{r} = \frac

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$3$ times the original

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(B) The surface area to volume ratio for a sphere is given by the formula: $\frac{SA}{V} = \frac{4 \pi r^2}{\frac{4}{3} \pi r^3} = \frac{3}{r} = \frac{6}{d}$,where $d$ is the diameter.For the initial state,$d_1 = 30 \, nm$,so the ratio is $\frac{6}{30} = 0.2 \, nm^{-1}$.For the final state,$d_2 = 10 \, nm$,so the ratio is $\frac{6}{10} = 0.6 \, nm^{-1}$.The ratio of the new value to the original value is $\frac{0.6}{0.2} = 3$.Thus,the surface area to volume ratio becomes $3$ times the original.

When the size of a spherical nanoparticle decreases from $30 \, nm$ to $10 \, nm$,the ratio of surface area to volume becomes:

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