the volume of an object is equal to the ratio of its mass to density, $v = \\frac{m}{d}$. the mass of a…

Explanation:

Step1: Calculate the volume of the grape

Given $V=\frac{m}{d}$, $m = 8.4$ grams and $d=2$ g/cm³. So $V=\frac{8.4}{2}=4.2$ cm³.

Step2: Use the volume - formula for a sphere

The volume formula for a sphere is $V=\frac{4}{3}\pi r^{3}$. We know $V = 4.2$ cm³, so $4.2=\frac{4}{3}\pi r^{3}$. First, solve for $r^{3}$: $r^{3}=\frac{4.2\times3}{4\pi}=\frac{12.6}{4\pi}$.

Step3: Calculate the value of $r$

$r=\sqrt[3]{\frac{12.6}{4\pi}}$. $r=\sqrt[3]{\frac{12.6}{4\times3.14}}\approx\sqrt[3]{\frac{12.6}{12.56}}\approx\sqrt[3]{1.0032}\approx1.0$ cm.

Answer:

1.0 cm