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Question

asked 2021-05-30

Find the volume V of the described solid S.

A cap of a sphere with radius r and height h.

V=?

A cap of a sphere with radius r and height h.

V=?

asked 2021-06-09

Change from rectangular to cylindrical coordinates. (Let \(r\geq0\) and \(0\leq\theta\leq2\pi\).)

a) \((-2, 2, 2)\)

b) \((-9,9\sqrt{3,6})\)

c) Use cylindrical coordinates.

Evaluate

\(\int\int\int_{E}xdV\)

where E is enclosed by the planes \(z=0\) and

\(z=x+y+10\)

and by the cylinders

\(x^{2}+y^{2}=16\) and \(x^{2}+y^{2}=36\)

d) Use cylindrical coordinates.

Find the volume of the solid that is enclosed by the cone

\(z=\sqrt{x^{2}+y^{2}}\)

and the sphere

\(x^{2}+y^{2}+z^{2}=8\).

a) \((-2, 2, 2)\)

b) \((-9,9\sqrt{3,6})\)

c) Use cylindrical coordinates.

Evaluate

\(\int\int\int_{E}xdV\)

where E is enclosed by the planes \(z=0\) and

\(z=x+y+10\)

and by the cylinders

\(x^{2}+y^{2}=16\) and \(x^{2}+y^{2}=36\)

d) Use cylindrical coordinates.

Find the volume of the solid that is enclosed by the cone

\(z=\sqrt{x^{2}+y^{2}}\)

and the sphere

\(x^{2}+y^{2}+z^{2}=8\).

asked 2021-05-03

Find the maximum volume of a rectangular box that is inscribed in a sphere of radius r.

asked 2021-03-09

The volume of a sphere is \(5,572.45 \in^3\) To the nearest inch, what is the radius of the sphere?