Content code
m1596
Slug (identifier)
the-volume-of-a-sphere
Grades
Secondary III
Topic
Mathematics
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Corps

The volume of a sphere corresponds to the space occupied inside it. To find its volume, simply apply the following formula.

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||V=\dfrac{4\pi r^3}{3}||where||\begin{align}V&:\text{Volume}\\ r&:\text{Radius of the sphere}\end{align}||

Corps

As with the area of a sphere, only the radius measurement is needed to calculate the volume of a sphere.

For the volume of a hemisphere, simply calculate the volume of the sphere and divide the result by 2.

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Corps

To keep the water in a swimming pool clean, a company manufactures chlorine granules in the shape of a sphere.

Image
Ball or sphere with its radius to determine the volume
Corps

Assuming that the granules are well-compacted so the loss of space is negligible, how many granules will fit into a |5\ 000\ \text{cm}^3| container?

  1. Identify the solid
    In this context, it is clearly mentioned that the solid is a sphere.

  2. Apply the formula
    ||\begin{align}V&=\dfrac{4\pi r^3}{3}\\\\&=\dfrac{4\pi(0.1)^3}{3}\\\\&\approx0.004\ \text{cm}^3\end{align}||

  3. Interpret the answer
    To determine the number of granules, all that remains is the following division.||5\ 000\ \text{cm}^3\div0.004\ \text{cm}^3/\text{granule}=1\ 250\ 000\ \text{granules}||There are |1\ 250\ 000\ \text{granules}| in a |5\ 000\ \text{cm}^3| container.

Corps

Finally, remember the relationship between the radius, height and width of a sphere

In some problems, we must find the measure of the radius when the volume is given. This is called finding a missing measure of a sphere from the volume.

 

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