The percent of the volume of the planet is the volume of its moon when the diameter of a planet is about 26,546 mi is 2.2%.
What is percentage of a number?
Percentage of a number is the part of the whole number which is expressed in the fraction of hundredth. It is represented with "%" symbol.
Volume of sphere is the amount of quantity, which is obtained by the it in the 3 dimensional space.
Volume of sphere can be given as,
[tex]V=\dfrac{4}{3}\pi \left( \dfrac{d}{2}\right)^3[/tex]
Here, (d) is the diameter of the sphere.
The diameter of a planet is about 26,546 mi. The volume of it is,
[tex]V_p=\dfrac{4}{3}\pi \left( \dfrac{26546}{2}\right)^3[/tex]
The diameter of the planet's moon is about 28% of the diameter of the planet. Thus, the diameter of the moon is,
[tex]d=\dfrac{28}{100}\times26546\\d=7432.88\rm\; mi[/tex]
The volume of moon is,
[tex]V_m=\dfrac{4}{3}\pi \left( \dfrac{7432.88}{2}\right)^3[/tex]
The percent of the volume of the moon is the volume of its planet,
[tex]P=\dfrac{\dfrac{4}{3}\pi \left( \dfrac{26546}{2}\right)^3-\dfrac{4}{3}\pi \left( \dfrac{7432.88}{2}\right)^3}{\dfrac{4}{3}\pi \left( \dfrac{26546}{2}\right)^3}\times100[/tex]
[tex]P=\dfrac{ \left( \dfrac{26546}{2}\right)^3-\left( \dfrac{7432.88}{2}\right)^3}{ \left( \dfrac{26546}{2}\right)^3}\times100\\P=97.80 \%[/tex]
For planet to moon, this percentage is 2.2%.
Thus, the percent of the volume of the planet is the volume of its moon when the diameter of a planet is about 26,546 mi is 2.2%.
Learn more about the percentage here;
https://brainly.com/question/2085058
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