The mass of an iron ball is 312 g. If the density of iron is 7.8 g/cm³, the volume of the ball is a. 40 cm³ b. 62.50 cm³ c. 100 cm³
The Correct Answer and Explanation is:
To find the volume of the iron ball, we can use the formula:Volume=MassDensity\text{Volume} = \frac{\text{Mass}}{\text{Density}}Volume=DensityMass
Given:
- Mass = 312 g
- Density = 7.8 g/cm³
Now plug the values into the formula:Volume=312 g7.8 g/cm3=40 cm3\text{Volume} = \frac{312 \, \text{g}}{7.8 \, \text{g/cm}^3} = 40 \, \text{cm}^3Volume=7.8g/cm3312g=40cm3
Correct answer: a. 40 cm³
Explanation:
The relationship between mass, volume, and density is a fundamental concept in physics and chemistry. Density describes how much mass exists in a given volume of a substance. The formula connecting these three properties is:Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}Density=VolumeMass
Rearranging this to solve for volume gives:Volume=MassDensity\text{Volume} = \frac{\text{Mass}}{\text{Density}}Volume=DensityMass
This problem gives the mass of an iron ball as 312 grams. The density of iron is 7.8 grams per cubic centimeter. By substituting these values into the volume formula, we divide 312 by 7.8. The units of grams cancel out, leaving the answer in cubic centimeters, which is a unit of volume.312÷7.8=40312 \div 7.8 = 40312÷7.8=40
So the iron ball occupies 40 cubic centimeters of space. This is a typical type of question used in science to test understanding of the density formula and unit conversions. It also emphasizes the importance of consistent units. In this case, mass is in grams and density in grams per cubic centimeter, so the resulting volume is naturally in cubic centimeters without needing any conversions.
