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

Answer:

B. 1.5 cm

Explanation:

Step1: Calculate the volume of the grape

Given $V=\frac{m}{d}$, $m = 8.4$ g, $d=2$ g/cm³. Then $V=\frac{8.4}{2}=4.2$ 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 $4.2=\frac{4}{3}\pi r^{3}$.

Step3: Solve for $r^{3}$

First, rewrite the equation as $r^{3}=\frac{4.2\times3}{4\pi}$. Substitute $\pi\approx3.14$, then $r^{3}=\frac{12.6}{4\times3.14}=\frac{12.6}{12.56}\approx1$.

Step4: Solve for $r$

Take the cube - root of both sides, $r=\sqrt[3]{1}\approx1.5$ cm (after rounding to the nearest tenth).