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krok68 [10]
3 years ago
8

Statements that are true for a cylinder with radius r and height h.

Mathematics
1 answer:
vampirchik [111]3 years ago
7 0

Answer:

Only the second and third statements are correct:

Doubling <em>r</em> quadruples the volume.

Doubling <em>h</em> doubles the volume.

Step-by-step explanation:

The volume of a cylinder is given by:

\displaystyle V=\pi r^2h

We can go through each statement and examine its validity.

Statement 1)

If the radius is doubled, our new radius is now 2<em>r</em>. Hence, our volume is:

\displaystyle V=\pi (2r)^2h=4\pi r^2h

So, compared to the old volume, the new volume is quadrupled the original volume.

Statement 1 is not correct.

Statement 2)

Using the previous reasonsing, Statement 2 is correct.

Statement 3)

If the height is doubled, our new height is now 2<em>h</em>. Hence, our volume is:

V=\pi r^2(2h)=2\pi r^2h

So, compared to the old volume, the new volume has been doubled.

Statement 3 is correct.

Statement 4)

Statement 4 is not correct using the previous reasonsing.

Statement 5)

Doubling the radius results in 2<em>r</em> and doubling the height results in 2<em>h</em>. Hence, the new volume is:

V=\pi (2r)^2(2h)=\pi (4r^2)(2h)=8\pi r^2h

So, compared to the old volume, the new volume is increased by eight-fold.

Statement 5 is not correct.

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