Final answer:
The radius of a cone with a volume of 201 cubic cm and a height of 12 cm is approximately 2.25 cm. This is calculated using the cone volume formula V = ⅓πr²h, solving for r after substituting the given volume and height.
Step-by-step explanation:
To find the radius of a cone with a given volume and height, you can use the formula for the volume of a cone, which is V = ⅓πr²h, where V is the volume, r is the radius, and h is the height. Here, we have a volume of 201 cubic cm and a height of 12 cm.
- First, write down the formula for the volume of a cone: V = ⅓πr²h.
- Insert the known values into the formula, giving us 201 = ⅓πr²(12).
- To find r, divide both sides by ⅓π and 12: r² = (201 × 3) / (π × 12).
- Calculate the right side to find r². After computation, r² = 201 × 3 / (3.14159 × 12) ≈ 5.0672 cm².
- Finally, take the square root of both sides to solve for r: r ≈ √5.0672 ≈ 2.25 cm.
The radius of the cone is approximately 2.25 cm.
You can think of a cone as a triangle which is being rotated about one of its vertices. Now, think of a scenario where we need to calculate the amount of water that can be accommodated in a conical flask. In other words, calculate the capacity of this flask. The capacity of a conical flask is basically equal to the volume of the cone involved. Thus, the volume of a three-dimensional shape is equal to the amount of space occupied by that shape.