Question

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 1

The answer is 1.0 cm.

Explanation:

The volume of the object is:

`V=(m)/(d).`

Where
`m` is mass of the object, and
`d` is its density.

Now for the spherical grape
`m=8.4` grams and
`d=2(grams)/(cm^3)`.

Therefore:

`V=(m)/(d)=(8.4grams)/(2(grams)/(cm^3))=4.2\:cm^3.`

Now since the grape is spherical, its volume is given by:

`V=(4)/(3) \pi r^3`

`\therefore r=\sqrt[3]{(3V)/(4\pi) }`

Substituting
`V=4.2cm^3` we get:

`r=\sqrt[3]{(3(4.2cm^3))/(4\pi) }=1.000891253\:cm,`

which to the nearest tenth of a centimeter is 1.0 cm, and therefore the radius of the grape is 1.0 cm.