Question

The volume of an object is equal to the ratio of its mass to density, V = . 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.

Answer 1

Radius of grape is 1 cm

Step-by-step explanation:

Mass = Volume x density

Mass = 8.4 gm

Density = 2.4 g/cc

Substituting

       8.4 = Volume x 2.4

       Volume = 3.5 cm³

$\texttt{Volume of sphere =}\frac{4}{3}\pi r^3$

We need to find radius, r

Substituting volume value

              $\texttt{Volume of sphere =}\frac{4}{3}\pi r^3=3.5\\\\r^3=0.836\\\\r=0.941cm=1cm$

Radius of grape = 1 cm  

Answer 2

Answer:

Radius of the grape, r = 1.0007 cm

Step-by-step explanation:

It is given that,

The density of an object is given by :

$\rho=\dfrac{m}{V}$

where

m = mass of the object

V = volume

Here, mass of the spherical grape, m = 8.4 grams

Density, $\rho=2\ g/cm^3$

So, $V=\dfrac{m}{\rho}$

$V=\dfrac{8.4\ g}{2\ g/cm^3}$

$V=4.2\ cm^3$

The volume of grape is given by :

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

r = radius of grape

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

$r^3=\dfrac{3\times 4.2\ cm^3}{4\pi}$

$r=(1.002)^{\dfrac{1}{3}}\ cm$

r = 1.0007 cm

So, the radius of the grape is 1.0007 cm. Hence, this is the required solution.