how does the volume of an oblique cylinder change if the radius is reduced to 2/9 of it's original size and the height is quadrupled?
v=16/81pir2h
v-2/81pir2h
how does the volume of an oblique cylinder if the radius is reduced 2/9 of its original size and the height is quadrupled?
To determine how the volume of an oblique cylinder changes when the radius is reduced to 2/9 of its original size and the height is quadrupled, you can follow these steps:
1. Start with the formula for the volume of a cylinder: V = πr^2h, where V is the volume, r is the radius, and h is the height.
2. Let's assume the original radius is denoted by r1 and the original height is denoted by h1.
3. Calculate the volume of the original oblique cylinder using the given values: V1 = πr1^2h1.
4. Substitute the values into the formula for the volume of the cylinder: V1 = π(r1/1)^2(h1/1).
5. Now, bring in the changes: r2 (new radius) = r1 * 2/9, and h2 (new height) = h1 * 4.
6. Substituting the new values into the formula: V2 = π(r2)^2(h2).
7. Replace r2 and h2 with the given values from step 5: V2 = π[(r1*2/9)^2][(h1*4)].
8. Simplify the equation: V2 = π(4/81)r1^2 * 4h1.
9. Simplify further: V2 = π(16/81)(r1^2h1).
10. Compare the two volumes to observe how they change: V2/V1 = (π(16/81)(r1^2h1))/(πr1^2h1).
11. Cancel out the similar terms: V2/V1 = 16/81.
Therefore, the volume of the oblique cylinder changes to 16/81 of its original volume. This reduction is irrespective of the specific values of the original radius and height.