Final answer:
To find the volume of a cone with the same radius and height as a given cylinder, you first need to find the volume of the cylinder. Once the volume of the cylinder is determined, you can use the formula for the volume of a cone to find the volume of the cone.
Step-by-step explanation:
To find the volume of a cone with the same radius and height as a cylinder, we first need to find the volume of the cylinder.
Given that the volume of the cylinder is 78 cm³ and using the formula V = πr²h, we can rearrange the formula to solve for the radius:
- V = πr²h
- 78 = 3.142 × r² × 5.25
- r² = 78 / (3.142 × 5.25)
- r² ≈ 4.998
- r ≈ √4.998 ≈ 2.236
Now, we can find the volume of the cone using the formula V = (1/3)πr²h:
- V = (1/3) × 3.142 × (2.236)² × 5.25
Calculating this gives us a volume of approximately 10.322 cm³ for the cone.