An ellipsoid has radii with lengths of $5$ $5$ , $7$ $7$ , and $7$ $7$ . A portion the size of a hemisphere with a radius of $5$ $5$ is removed from the ellipsoid. What is the remaining volume of the ellipsoid?

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An ellipsoid has radii with lengths of $5$ $5$ , $7$ $7$ , and $7$ $7$ . A portion the size of a hemisphere with a radius of $5$ $5$ is removed from the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2017-04-24T13:52:36

The remaining volume is $\frac{730}{3} π$ $730/3pi$ or $764.06$ $764.06$ .

Explanation:

To determine the remaining volume of the ellipsoid, we need to subtract the volume of the hemisphere from the volume of the ellipsoid.

The formula for volume of an ellipsoid is:
$V_{E} = \frac{4}{3} π a b c$ $V_E=4/3piabc$ , where $V_{E} =$ $V_E=$ Volume of ellipsoid, $π = 3.14$ $pi=3.14$ , and $a$ $a$ , $b$ $b$ , and $c$ $c$ are the radii.

The formula for volume of a hemisphere is:
$V_{H} = \frac{2}{3} π r^{3}$ $V_H=2/3pir^3$ , where $V_{H} =$ $V_H=$ Volume of hemisphere, $π = 3.14$ $pi=3.14$ , and $r =$ $r=$ radius.

Hence the remaining volume of the ellipsoid will be:

$V_{E} - V_{H} = \frac{4}{3} π a b c - \frac{2}{3} π r^{3}$ $V_E-V_H=4/3piabc-2/3pir^3$

$V_{E} - V_{H} = \frac{2}{3} π (2 a b c - r^{3})$ $V_E-V_H=2/3pi(2abc-r^3)$

$V_{E} - V_{H} = \frac{2}{3} π ([2 \times 5 \times 7 \times 7] - [5^{3}])$ $V_E-V_H=2/3pi([2xx5xx7xx7]-[5^3])$

$V_{E} - V_{H} = \frac{2}{3} π (490 - 125)$ $V_E-V_H=2/3pi(490-125)$

$V_{E} - V_{H} = \frac{2}{3} π \times 365$ $V_E-V_H=2/3pixx365$

$V_{E} - V_{H} = \frac{730}{3} π$ $V_E-V_H=730/3pi$

$V_{E} - V_{H} = \frac{730}{3} \times 3.14$ $V_E-V_H=730/3xx3.14$

$V_{E} - V_{H} = 764.06$ $V_E-V_H=764.06$

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An ellipsoid has radii with lengths of $5$ $5$ , $7$ $7$ , and $7$ $7$ . A portion the size of a hemisphere with a radius of $5$ $5$ is removed from 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 $5$ $5$ , $7$ $7$ , and $7$ $7$ . A portion the size of a hemisphere with a radius of $5$ $5$ is removed from the ellipsoid. What is the remaining volume of the ellipsoid?