Question

the volume of an object is equal to the ratio of its mass to density, v = \frac{m}{d}. the mass of a spherical grape is 8.4 grams and its density is 2 grams per cubic centimeter. what is the radius of the grape? round to the nearest tenth of a centimeter. 1.0 cm 1.5 cm 1.9 cm 2.1 cm

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 $\frac{4}{3}\pi r^{3}=4.2$.
First, solve for $r^{3}$: $r^{3}=\frac{4.2\times3}{4\pi}=\frac{12.6}{4\pi}$.

Step3: Calculate the value of $r$

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

Answer:

1.0 cm