Final answer:
To find the height of the cone, use the formula V = (1/3)πr²h and solve for h. Given the volume and the diameter of the base, calculate the radius. Plug in the known values to find the height
Step-by-step explanation:
To find the height of the cone, we can use the formula for the volume of a cone: V = (1/3)πr²h, where V is the volume, r is the radius of the base, and h is the height.
Given that the volume of the cone is 529.88 cm³ and the diameter of the base is 15 cm, we can calculate the radius of the base by dividing the diameter by 2: r = 15 cm / 2 = 7.5 cm.
Now, we can rearrange the formula to solve for h: h = 3V / (πr²). Plugging in the known values, we get h = (3 * 529.88 cm³) / (3.142 * (7.5 cm)²).
Calculating this equation, we find that h ≈ 11 cm.