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How do you find the volume of the sphere in terms of \[\pi \] given \[V=\dfrac{4}{3}\pi {{r}^{3}}\] and \[r=1.5m\]?

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Last updated date: 25th Feb 2024
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IVSAT 2024
Answer
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Hint: From the question given, we have been asked to find the volume of sphere in terms of \[\pi \].Given, \[V=\dfrac{4}{3}\pi {{r}^{3}}\] and \[r=1.5m\].We can find the volume of the sphere by using the formula which is already given in the question itself. We have to simply substitute the value of radius in the formula to get the volume of the sphere in terms of \[\pi \].

Complete step by step answer:
From the question itself we had been given that \[V=\dfrac{4}{3}\pi {{r}^{3}}\]
We have been also given the value of \[r\] in the question.
As we have discussed earlier, we have to simply substitute the value of \[r\] in the above formula to get the volume.
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By substituting the value of \[r\] which has been already given in the question, we get
\[V=\dfrac{4}{3}\pi {{r}^{3}}\]
\[\Rightarrow V=\dfrac{4}{3}\pi {{\left( 1.5m \right)}^{3}}\]
We have to further simplify the above equation to get the accurate value.
By further more simplifying the above question, we get
\[\Rightarrow V=\dfrac{4}{3}\pi \left( 3.375{{m}^{3}} \right)\]
On furthermore simplifying the above equation, we get \[\Rightarrow V=4.5\pi {{m}^{3}}\]
We should not substitute the value of \[\pi \] in the above equation, as in the question it have been asked to find the volume in terms of \[\pi \]
Therefore, Volume of the sphere in terms of \[\pi \] has been found.

Note: We should be well aware of the formulae of mensuration. Also, we should be very careful while doing the calculation. Also, we should read the question correctly as some conditions are given in the question. In this question it has been given that the answer should be in terms of \[\pi \]. So, we should carefully observe the question. Similarly we have formulae to find the volume of a cylinder given as $\pi {{r}^{2}}h$ and many more shapes.
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