3 years ago

The result of a horizontal cross-section of a pryramid

Mathematics

1 answer:

ladessa [460]3 years ago

7 0

Answer:

C rectangle

Step-by-step explanation:

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Find the volume of the ellipsoid x2+y2+4z2=100x2+y2+4z2=100.

kondor19780726 [428]

Given the ellipsoid $x^2+y^2+4z^2=100$

For the radius in the x-dirextion, y = z = 0, and we have

$x^2=100 \\ \\ \Rightarrow x=\pm10$

For the radius in the y-dirextion, x = z = 0, and we have

$y^2=100 \\ \\ \Rightarrow y=\pm10$

For the radius in the z-dirextion, x = y = 0, and we have

$4z^2=100 \\ \\ \Rightarrow z^2=25 \\ \\ \Rightarrow z=\pm5$

Thus, the radius of the ellipsoid is given by

$Volume=4\pi r^3=4\pi\times10\times10\times5=500\pi$

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