a cylinder has a volume of 19cm^3. If the radius is doubled, what is the volume of the new cylinder? HOW TO DO THIS
volume is proportional to height*radius^2
double radius, volume is quadrupled
19*4 cm^3
so answer is 1216
To find the new volume of the cylinder after doubling the radius, you can follow these steps:
1. Determine the original radius and volume of the cylinder. Let's assume the original radius is denoted as "r" and the original volume is given as 19 cm³.
2. Use the formula for calculating the volume of a cylinder: V = πr²h, where V represents the volume, π is a mathematical constant approximately equal to 3.14159, and h denotes the height of the cylinder.
3. Since we want to find the new volume after doubling the radius, we need to first determine the new radius. The new radius will be 2 times the original radius, so the new radius is 2r.
4. Substitute the values of the new radius (2r) and the original volume (19 cm³) into the formula: 19 = π(2r)²h.
5. To simplify the equation, square the value of 2r to get 4r². The equation becomes: 19 = π(4r²)h.
6. Divide both sides of the equation by 4π to isolate the term "r²h": (19 / (4π)) = r²h.
7. Simplify the left side of the equation by dividing 19 by 4π: (19 / (4π)) ≈ 1.52 cm³.
8. Now we know that r²h is equal to approximately 1.52 cm³.
Therefore, the volume of the new cylinder with the doubled radius is 1.52 cm³.