How to find the mass of a sphere?
Understand the Problem
The question is asking how to calculate the mass of a sphere. To determine the mass, we typically need to know the volume of the sphere and its density. The volume can be found using the formula V = (4/3)πr³, where r is the radius of the sphere. Then, we can use the formula mass = density × volume.
Answer
The mass of the sphere is $m = \text{density} \times \left(\frac{4}{3} \pi r^3\right)$.
Answer for screen readers
The mass of the sphere can be expressed as $m = \text{density} \times \left(\frac{4}{3} \pi r^3\right)$.
Steps to Solve
- Calculate the Volume of the Sphere
First, use the formula for the volume of a sphere, which is given by
$$ V = \frac{4}{3} \pi r^3 $$
where ( r ) is the radius of the sphere. Substitute the radius value into the formula to find the volume.
- Use the Density to Find Mass
Once you have the volume, you can find the mass using the formula
$$ m = \text{density} \times V $$
where ( m ) is the mass and ( V ) is the volume calculated in the previous step. Substitute the density and volume values to find the mass.
The mass of the sphere can be expressed as $m = \text{density} \times \left(\frac{4}{3} \pi r^3\right)$.
More Information
To find the mass of a solid sphere, knowing both the density and radius is crucial. The formula allows you to calculate it easily. Remember that the units for density should match the units you want for mass.
Tips
- Forgetting to convert units: Ensure that the radius and density are in compatible units before calculating the mass.
- Miscalculating volume: Double-check the calculation of the volume using the correct formula.
- Overlooking the density value: Make sure to use the correct value for density as it significantly affects the mass.
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