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-dime…

Question

asked Oct 12, 2019 78.6k views

1 Answer

Judge Maygarden · Answer 1 · 2019-10-18T14:53:30+0000

Answer:

1526.0 cubic units

Explanation:

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

$KA=√((6-0)^2+(0-0)^2)=6,\\ \\KL=√((0-0)^2+(9-0)^2)=9.$

The volume of the cylinder is

$V_(cylinder)=\pi r^2\cdot H.$

Then

$V_(cylinder)=\pi \cdot 9^2\cdot 6=486\pi \approx 1526.0\ un^3.$