Final answer:
To find the volume of a cone with a radius of 0.750 cm and a height of 5.25 cm, use the formula V = (1/3)π(0.750 cm)²(5.25 cm), giving a simplified result of approximately 0.984375π cm³ in terms of pi.
Step-by-step explanation:
To find the volume of the cone, we use the formula V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height. The provided formula V = πr²h is for the volume of a cylinder, not a cone. To calculate the volume of a cone, we need to multiply the base area (πr²) by the height (h) and then divide by 3, since a cone's volume is one-third the volume of a cylinder with the same base and height.
If a cone has a radius of 0.750 cm and a height of 5.25 cm, the formula would be applied as follows:
V = (1/3)π(0.750 cm)²(5.25 cm)
V = (1/3)π(0.5625 cm²)(5.25 cm)
V = (1/3)π(2.953125 cm³)
V = π·(2.953125 cm³)/3
V = 0.984375π cm³ (simplified answer in terms of π)
Therefore, the volume of the cone in terms of π is approximately 0.984375π cm³.