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. Substitute the values into the formula: $V=\frac{8.4}{2}=4.2$ 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 we can solve for $r$. First, rewrite the formula for $r$: $r^{3}=\frac{3V}{4\pi}$. Substitute $V = 4.2$ cm³ into the formula: $r^{3}=\frac{3\times4.2}{4\pi}=\frac{12.6}{4\pi}$. $r^{3}=\frac{12.6}{4\times3.14}=\frac{12.6}{12.56}\approx1$. Then, take the cube - root of both sides: $r=\sqrt[3]{1}\approx1.0$ cm

Answer:

1.0 cm