If the height of a cylinder is made nine times longer, how many times the volume of the original figure is the volume of the
new figure?
Since v = pi*r^2 * h, replacing h with 9h gives
pi * r^2 * 9h = 9 pi * r^2 * h = 9v
If the height of a cylinder is made nine times longer, the volume of the new figure will be nine times the volume of the original figure.
To determine how many times the volume of the new figure is compared to the original figure, we need to understand the relationship between the volume and the height of a cylinder.
The formula for the volume of a cylinder is V = πr²h, where V represents the volume, r is the radius, and h is the height.
Now, let's assume that the original height of the cylinder is represented by h1, and the new height is represented by h2. According to the problem, the new height is nine times longer than the original height, so we have h2 = 9h1.
To find how many times the volume of the new figure is compared to the original figure, we can calculate the ratio of the two volumes V2/V1.
Since the radius, r, is constant, we can ignore it for this calculation. Thus, the formula becomes V2/V1 = (πr²h2) / (πr²h1).
By cancelling out the common terms, the formula simplifies to V2/V1 = h2/h1.
Now, substituting the values h2 = 9h1, we get V2/V1 = 9h1 / h1.
Simplifying further, we find that V2/V1 = 9.
Therefore, the volume of the new figure is nine times greater than the volume of the original figure.