the volume of an object is equal to the ratio of its mass to density, v = \\(\\frac{m}{d}\\). the mass of a…
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
Answer
Explanation:
Step1: Calculate the volume
Given $m = 8.4$ grams and $d=2$ g/cm³, use $V=\frac{m}{d}$. $V=\frac{8.4}{2}=4.2$ 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 solve for $r$. $4.2=\frac{4}{3}\pi r^{3}$ First, isolate $r^{3}$: $r^{3}=\frac{4.2\times3}{4\pi}=\frac{12.6}{4\pi}$ $r^{3}=\frac{12.6}{4\times3.14}\approx1.003$ Then find $r$: $r=\sqrt[3]{1.003}\approx1.0$ cm
Answer:
1.0 cm