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A rectangle with vertices A(6, 0), K(0,0), L(0,9), and M(6, 9) is rotated around the x-axis. To the nearest tenth of a cubic unit, what is the volume of the resulting three-dimensional figure? Approximate as 3.14.

Respuesta :

frika

Answer:

1526.0 cubic units

Step-by-step explanation:

Rotating rectangle AKLM you will get cylinder with height KA and base radius KL.  From the given data

[tex]KA=\sqrt{(6-0)^2+(0-0)^2}=6,\\ \\KL=\sqrt{(0-0)^2+(9-0)^2}=9.[/tex]

The volume of the cylinder is

[tex]V_{cylinder}=\pi r^2\cdot H.[/tex]

Then

[tex]V_{cylinder}=\pi \cdot 9^2\cdot 6=486\pi \approx 1526.0\ un^3.[/tex]