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An ellipsoid has radii with lengths of $8$ $8$ , $3$ $3$ , and $4$ $4$ . A portion the size of a hemisphere with a radius of $2$ $2$ is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

1 Answer

Dec 29, 2016

$368.61$ $368.61$ cubic units (approximately)

Explanation:

Formulae you need to remember:
$XXX {Volume}_{ellipsoid} = \frac{4}{3} π \cdot r_{x} \cdot r_{y} \cdot r_{z}$ $color(white)("XXX")"Volume"_("ellipsoid")= 4/3 pi * r_x * r_y * r_z$

$XXX {Volume}_{sphere} = \frac{4}{3} π \cdot r^{3}$ $color(white)("XXX")"Volume"_("sphere")= 4/3 pi * r^3$

Given ellipsoid has a volume of $\frac{4}{3} π (8 \times 3 \times 4) = \frac{4}{3} π \cdot 96$ $4/3pi(8xx3xx4) = 4/3pi * 96$

Given sphere has a volume of $\frac{4}{3} π (2^{2}) = \frac{4}{3} π \cdot 8$ $4/3pi (2^2) = 4/3pi *8$

Volume of ellipsoid with sphere removed:
$XXX \frac{4}{3} π \cdot (96 - 8) = \frac{352}{3} π \approx 368.61$ $color(white)("XXX")4/3pi* (96-8) = 352/3 pi ~~368.61$

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