Marenonigt

Answered

2021-12-18

Consider the solid in xyz-space, which contains all points (x, y, z) whose z-coordinate satisfies

$0\le z\le 4-{x}^{2}-{y}^{2}$

Which statements do hold?

a) The solid is a sphere

b) The solid is apyramid

c) Its volume is$8\pi$

d) Its volume is$\frac{16\pi}{3}$

Which statements do hold?

a) The solid is a sphere

b) The solid is apyramid

c) Its volume is

d) Its volume is

Answer & Explanation

Carl Swisher

Expert

2021-12-19Added 28 answers

Step 1

Change in folar co-ordinates, tre get

Let

Carl Swisher

Expert

2021-12-20Added 28 answers

Here, take limit:

And we know,

So,

For each value of

Now, volume in

nick1337

Expert

2021-12-28Added 573 answers

Step 1

Consider the solid in xyz-space which contains all points (x,y,z) whose z-coordinate satisfies

Step 2

The solid is paraboloid.

We use cylindrical coordinates

and

The volume of the solid is given by

Thus, volume of the solid is

Hence, option (c) is correct.

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