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. 1.0 cm 1.5 cm 1.9 cm 2.1 cm

Explanation:

Step1: Calculate the volume

Given \(V=\frac{m}{d}\), \(m = 8.4\) grams and \(d=2\) grams per cubic centimeter.
\(V=\frac{8.4}{2}=4.2\) \(cm^{3}\)

Step2: Use the volume formula for a sphere

The volume formula for a sphere is \(V=\frac{4}{3}\pi r^{3}\).
Substitute \(V = 4.2\) into the formula: \(4.2=\frac{4}{3}\pi r^{3}\)

Step3: Solve for \(r^{3}\)

First, \(r^{3}=\frac{4.2\times3}{4\pi}\)
\(r^{3}=\frac{12.6}{4\pi}\approx\frac{12.6}{4\times3.14}\approx\frac{12.6}{12.56}\approx1.0\)

Step4: Solve for \(r\)

Take the cube - root of both sides: \(r=\sqrt[3]{1.0}\approx1.0\)

Answer:

1.0 cm