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If the radius of a cylinder is doubled while keeping the volume constant, the height must decrease to accommodate the increased cross-sectional area. Since the volume of a cylinder is calculated as ( V = \pi r^2 h ), doubling the radius (to ( 2r )) results in an area increase by a factor of four (( \pi (2r)^2 = 4\pi r^2 )). To maintain the same volume, the height must be reduced to one-fourth of the original height.
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What happens to the volume of a cylinder if the height is doubled and the diameter of the base is not changed?
since the volume of a right cylinder is height x area of base, the area of the baseis Pi * r^2 (r is radius which is 1/2 of diameter), so the area of the base did notchange, while the height is doubled so the volume is doubled.
How does the volume of a cylinder change if its height is doubled and its radius is halved?
The volume of a cylinder is calculated using the formula ( V = \pi r^2 h ), where ( r ) is the radius and ( h ) is the height. If the height is doubled and the radius is halved, the new volume becomes ( V' = \pi \left(\frac{r}{2}\right)^2 (2h) = \pi \left(\frac{r^2}{4}\right)(2h) = \frac{\pi r^2 h}{2} ), which is half the original volume. Thus, the volume of the cylinder decreases to 50% of its original size.
Does the area of a piece of paper change if you change the height and radius?
Yes.
How does the surface area of a rectangular prism change when the length and width and height are doubled?
if length and width are doubled then the volume should mulitiply by 8
What happens to a circle when the radius is doubled?
The area quadruples.
The volume of a circular cylinder varies directly with the height of the cylinder and with the square of the cylinder's radius If the height is halved and the radius is doubled then the volume will be?
The volume of a circular cylinder varies directly with the height of the cylinder and with the square of the cylinder's radius If the height is halved and the radius is doubled then the volume will be increased.
If the radius and height of a cylinder are doubled then its lateral are?
quadrupled. :)
What is the new volume of a cylinder if the height and radius are doubled?
If the radius and height of a cylinder are both doubled, then its surface area becomes 4 times what it was originally, and its volume becomes 8 times as much.
If the height and radius of a cylinder are doubled how will the volume of the cylinder be affected?
volume is related as radius squared x height soif both radius and height doubled volume increases 2 x 2 x 2 = 8 times
How does the volume of a cylinder change if the height is doubled?
The volume will be doubled.
How does the volume of a cylinder change if the radius is doubled?
It is quadrupled. volume_cylinder = π x radius2 x height If radius → 2 x radius then: new_volume = π x (2 x radius)2 x height = π x 22 x radius2 x height = 4 x π x radius2 x height = 4 x original_volume
What happens to the radius if the volume of a cylinder is doubled?
It depends on whether the height remains unchanged or increases in the same proportion as the radius.
How does the area of a triangle change when the height is doubled?
If the base stays the same, the area is also doubled.
What happens to the volume of a cylinder if the height is doubled and the diameter of the base is not changed?
since the volume of a right cylinder is height x area of base, the area of the baseis Pi * r^2 (r is radius which is 1/2 of diameter), so the area of the base did notchange, while the height is doubled so the volume is doubled.
How does the volume of a cylinder change if its height is doubled and its radius is halved?
The volume of a cylinder is calculated using the formula ( V = \pi r^2 h ), where ( r ) is the radius and ( h ) is the height. If the height is doubled and the radius is halved, the new volume becomes ( V' = \pi \left(\frac{r}{2}\right)^2 (2h) = \pi \left(\frac{r^2}{4}\right)(2h) = \frac{\pi r^2 h}{2} ), which is half the original volume. Thus, the volume of the cylinder decreases to 50% of its original size.
Does the area of a piece of paper change if you change the height and radius?
Yes.
How many times larger is the new volume of a cylinder if only the height doubled and the radius remained the same?
Two times larger.
