An ellipsoid has radii with lengths of $15$ $15$ , $12$ $12$ , and $9$ $9$ . A portion the size of a hemisphere with a radius of $7$ $7$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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An ellipsoid has radii with lengths of $15$ $15$ , $12$ $12$ , and $9$ $9$ . A portion the size of a hemisphere with a radius of $7$ $7$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2018-07-13T23:43:15

$6067.4626\ \text{unit}^3$

Explanation:

The remaining volume of the ellipsoid will be equal to the difference of volume of original ellipsoid with radii $a=15$ , $b=12$ & $c=9$ & the volume of hemi-sphere of radius $r=7$ hence the remaining volume of ellipsoid

$\frac{4\pi}{3}abc-2/3\pir^3$

$=\frac{4\pi}{3}(15)(12)(9)-2/3\pi(7)^3$

$=\frac{5794\pi}{3}$

$=6067.4626\ \text{unit}^3$

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An ellipsoid has radii with lengths of $15$ $15$ , $12$ $12$ , and $9$ $9$ . A portion the size of a hemisphere with a radius of $7$ $7$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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An ellipsoid has radii with lengths of 15 1515 , 12 1212 , and 9 99 . A portion the size of a hemisphere with a radius of 7 77 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Explanation:

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An ellipsoid has radii with lengths of $15$ $15$ , $12$ $12$ , and $9$ $9$ . A portion the size of a hemisphere with a radius of $7$ $7$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?