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How does the volume of a cone change when the radius is quadrupled and the height is reduced to one over five of its original size?
The volume ( V ) of a cone is given by the formula ( V = \frac{1}{3} \pi r^2 h ). When the radius is quadrupled, it becomes ( 4r ), and when the height is reduced to one-fifth, it becomes ( \frac{h}{5} ). Substituting these changes into the volume formula gives ( V' = \frac{1}{3} \pi (4r)^2 \left(\frac{h}{5}\right) = \frac{1}{3} \pi (16r^2) \left(\frac{h}{5}\right) = \frac{16}{5} V ). Thus, the new volume is ( \frac{16}{5} ) times the original volume.
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How does the volume of an cylinder change if the radius is reduced to of its original size and the height is quadrilpled?
This could have been an intriguing little exercise if you hadn't left the fraction out of the question. (If the fraction was supposed to be 1/2 then the answer is "No change".)
How does the height change if the radius is doubled?
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.
If the dimension of a box is quadrupled how are the surface area and volume affected?
The question is not clear about how many of the three dimensions of the box are quadruples. For example, you could quadruple its height but leave the length and breadth unchanged.However, if you assume that all three dimensions are quadrupled, the surface area is 16 times as large and the volume is 64 times as great.
What is the effect on the volume of a rectangular prism if the width is doubled and the height is reduced to half the original height?
If the width of a rectangular prism is doubled and the height is reduced to half, the new volume can be calculated by adjusting the original volume formula ( V = l \times w \times h ). Doubling the width increases it to ( 2w ), while halving the height reduces it to ( \frac{h}{2} ). The new volume becomes ( V' = l \times (2w) \times \left(\frac{h}{2}\right) = l \times w \times h = V ). Thus, the volume remains unchanged.
How does the area of a triangle change if the base is doubled and the height is halved?
you can easely calculate it: the original measurements: 6(bottom)*6(height)*½=18 double the base half the height: 12*3*½=18 so it remains the same
How does a volume of a rectangular prism change is the length and width is doubled and the height stays the same?
It is quadrupled.
If the radius and height of a cylinder are doubled then its lateral are?
quadrupled. :)
What happens to the area of a parallelogram when you double the height and the base?
The area of the parallelogram is quadrupled.
How does the volume of an cylinder change if the radius is reduced to of its original size and the height is quadrilpled?
This could have been an intriguing little exercise if you hadn't left the fraction out of the question. (If the fraction was supposed to be 1/2 then the answer is "No change".)
If the length of a rectangle is doubled and its height quadrupled how is its area changed?
Its area is now eight times greater than its original size. If area = L x H, then 2(L) x (4)H = 8 (original area)
What happens to the area of a parallelogram when you double both the height and the base?
The area of the parallelogram is quadrupled.
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
How do you compare the original height of a ball with its rebound height?
The height to which a dropped ball rebounds is typically significantly greater than the height of the ball. Also, incidentally, the height of the ball usually doesn't change during the event, and remains equal to its original height.
What is the area of a parallelogram if the base and height are doubled?
As area_of_parallelogram = base x height if they are both doubled then: new_area = (2 x base) x (2 x height) = 4 x (base x height) = 4 x area_of_parallelogram Thus, if the base and height of a parallelogram are [both] doubled, the area is quadrupled.
How tall are the polly pocket dolls?
The original Polly pocket dolls are about a centimeter in height. The newer Polly pocket dolls ( the ones where you can change their clothes) are about three inches in height
What will happen to the potential energy if the height is reduced into half?
If the height is reduced by half, the potential energy will also be reduced by half. This is because potential energy is directly proportional to the height of an object above a reference point, following the equation PE = mgh, where m is mass, g is acceleration due to gravity, and h is height.
If the dimension of a box is quadrupled how are the surface area and volume affected?
The question is not clear about how many of the three dimensions of the box are quadruples. For example, you could quadruple its height but leave the length and breadth unchanged.However, if you assume that all three dimensions are quadrupled, the surface area is 16 times as large and the volume is 64 times as great.
