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[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
What is the volume of a sphere with a diameter of 32.5 m, rounded to the nearest tenth of a cubic meter (m³)?
[tex]\dashrightarrow\large\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
We are asked to find the volume of a sphere, which we can find using the following formula:-
[tex]\bold{V=\dfrac{4}{3} \pi r^3}[/tex]
Where:-
- V=volume
- π=pi (3.14…)
- r=radius
Provided information:-
What we need in order to find the volume:-
What we need in order to find the radius:-
- Since the radius is exactly one-half of the diameter, we divide the diameter by 2 in order to find the radius:-
[tex]\bold{r=d\div2}[/tex]
Replace d with 32.5:-
[tex]\bold{r=32.5\div2}[/tex]
Therefore, the sphere's radius is as follows:-
[tex]\bold{r=16.25}[/tex] m
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Now, let's find the sphere's volume, which, as I mentioned earlier, can be found with the help of this formula:-
[tex]\bold{V=\dfrac{4}{3} \pi r^3}[/tex]
Replace r with 16.25:-
[tex]\bold{V=\dfrac{4}{3} \pi (4291)}[/tex] Next, we replace π with 3.14:-
[tex]\bold{V=\dfrac{4}{3} \times3.14\times4291}[/tex]
On simplification,
[tex]\bold{V=\dfrac{4}{3} \times13,473.74}[/tex]
On further simplification,
[tex]\bold{V=17,964.9\:m^3}\Longleftarrow\sf{volume\:of\:the\:sphere}[/tex]
Good luck with your studies.
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