the volume of an object is equal to the ratio of its mass to its density V equals m over d the mass of a spherical grape is 8.4 grams and has a density of 2 grams per cubic centimeter what is the radius of the grape round to the nearest tenth of a centimeter

Answer:The answer is 1.0 cm.Step-by-step explanation:The volume of the object is: [tex]V=\frac{m}{d}.[/tex]Where [tex]m[/tex] is mass of the object, and [tex]d[/tex] is its density. Now for the spherical grape [tex]m=8.4[/tex] grams and [tex]d=2\frac{grams}{cm^3}[/tex].Therefore: [tex]V=\frac{m}{d}=\frac{8.4grams}{2\frac{grams}{cm^3}}=4.2\:cm^3.[/tex]Now since the grape is spherical, its volume is given by:[tex]V=\frac{4}{3} \pi r^3[/tex][tex]\therefore r=\sqrt[3]{\frac{3V}{4\pi} }[/tex]Substituting [tex]V=4.2cm^3[/tex] we get:[tex]r=\sqrt[3]{\frac{3(4.2cm^3)}{4\pi} }=1.000891253\:cm,[/tex]which to the nearest tenth of a centimeter is 1.0 cm, and therefore the radius of the grape is 1.0 cm.