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, $d=2$ g/cm³. Then $V=\frac{8.4}{2}=4.2$ cm³.

Step2: Use the volume - formula of a sphere

The volume formula of a sphere is $V = \frac{4}{3}\pi r^{3}$. We know $V = 4.2$ cm³, so $\frac{4}{3}\pi r^{3}=4.2$.

Step3: Solve for $r$

First, $r^{3}=\frac{4.2\times3}{4\pi}=\frac{12.6}{4\pi}$. Then $r=\sqrt[3]{\frac{12.6}{4\pi}}$. Substitute $\pi\approx3.14$, $r=\sqrt[3]{\frac{12.6}{4\times3.14}}=\sqrt[3]{\frac{12.6}{12.56}}\approx\sqrt[3]{1}\approx1.0$ cm.

Answer:

1.0 cm