An ellipsoid has radii with lengths of $6$ $6$ , $6$ $6$ , and $3$ $3$ . A portion the size of a hemisphere with a radius of $6$ $6$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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An ellipsoid has radii with lengths of $6$ $6$ , $6$ $6$ , and $3$ $3$ . A portion the size of a hemisphere with a radius of $6$ $6$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2016-11-12T17:08:09

Remaining volume is $0$ $0$

Explanation:

Volume of an ellipsoid with dimensions $a$ $a$ , $b$ $b$ and $c$ $c$ is given by $\frac{4}{3} π \times a \times b \times c$ $4/3pixxaxxbxxc$ , hence

volume of ellipsoid of radii with lengths of $6$ $6$ , $6$ $6$ and $3$ $3$ is $\frac{4}{3} \times π \times 6 \times 6 \times 3 = 144 π$ $4/3xxpixx6xx6xx3=144pi$ .

Now as volume of sphere is given by $\frac{4}{3} π r^{3}$ $4/3pir^3$ , volume of hemisphere of radius $6$ $6$ cut from this is $\frac{1}{2} \times \frac{4}{3} π \times 6^{3} = \frac{2}{3} \times 216 π = 144 π$ $1/2xx4/3pixx6^3=2/3xx216pi=144pi$

Hence, remaining volume of the ellipsoid is $144 π - 144 π = 0$ $144pi-144pi=0$

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An ellipsoid has radii with lengths of $6$ $6$ , $6$ $6$ , and $3$ $3$ . A portion the size of a hemisphere with a radius of $6$ $6$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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An ellipsoid has radii with lengths of $6$ $6$ , $6$ $6$ , and $3$ $3$ . A portion the size of a hemisphere with a radius of $6$ $6$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?