Final answer:
To estimate the height of the cone, its volume formula was rearranged and the known values were substituted to find the height, resulting in an estimate of approximately 6.75 cm.
Step-by-step explanation:
To solve for the height of a cone given its radius and volume, we can employ 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. We know the cone's volume is 102 cm³ and the radius is 4.96 cm. By substituting these values into the volume formula, we get 102 cm³ = ⅓π(4.96 cm)²h. Solving for h, we obtain h = ×(102 cm³) / (⅓π(4.96 cm)²).
Calculating further, h = ×(102 cm³) / (⅓(3.14159)(4.96 cm)²) ≈ ×(102 cm³) / (51.836 cm²) ≈ 1.968 cm.
After calculating, we see that the closest estimate for h from the given options is 6.75 cm.
Thus, the estimate for h is approximately 6.75 cm.