Photo AI

Iron has a density of 7.87 g cm³ - Leaving Cert Physics - Question (a) - 2022

Question icon

Question (a)

Iron-has-a-density-of-7.87-g-cm³-Leaving Cert Physics-Question (a)-2022.png

Iron has a density of 7.87 g cm³. An iron sphere has a mass of 500 g. Calculate the radius of the sphere in cm.

Worked Solution & Example Answer:Iron has a density of 7.87 g cm³ - Leaving Cert Physics - Question (a) - 2022

Step 1

Calculate the Volume of the Sphere

96%

114 rated

Answer

To find the volume of the sphere, we use the formula for density:

ρ=mV\rho = \frac{m}{V}

Where:

  • ( \rho ) is the density,
  • ( m ) is the mass,
  • ( V ) is the volume.

Rearranging the formula to find the volume yields:

V=mρV = \frac{m}{\rho}

Substituting the values:

  • Mass (m) = 500 g
  • Density (( \rho )) = 7.87 g cm³

V=5007.87≈63.53 cm3V = \frac{500}{7.87} \approx 63.53 \text{ cm}^3

Step 2

Calculate the Radius of the Sphere

99%

104 rated

Answer

The formula for the volume of a sphere is:

V=43πr3V = \frac{4}{3} \pi r^3

To find the radius (r), we rearrange the formula:

r=(3V4π)13r = \left( \frac{3V}{4\pi} \right)^{\frac{1}{3}}

Substituting the volume we calculated:

r=(3×63.534π)13≈2.475 cmr = \left( \frac{3 \times 63.53}{4\pi} \right)^{\frac{1}{3}} \approx 2.475 \text{ cm}

Join the Leaving Cert students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;