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. \bigcirc 1.0 cm \bigcirc 1.5 cm \bigcirc 1.9 cm \bigcirc 2.1 cm

Explanation:

Step1: Calculate grape volume

$V = \frac{m}{d} = \frac{8.4}{2} = 4.2$ cm³

Step2: Set up sphere volume formula

$V = \frac{4}{3}\pi r^3$

Step3: Solve for $r$

Rearrange formula: $r = \sqrt[3]{\frac{3V}{4\pi}}$
Substitute $V=4.2$:
$r = \sqrt[3]{\frac{3\times4.2}{4\times3.1416}} = \sqrt[3]{\frac{12.6}{12.5664}} \approx \sqrt[3]{1.0027} \approx 1.0$

Answer:

1.0 cm