Answer:
4.0 cm
Explanation:
The volume of the frustum is the volume of the full cone (with height y + 7) minus the volume of the upper smaller cone (with height y).
Formula:
volume of cone = (1/3)πr²h
For the full cone:
r = 8 cm
h = y + 7
volume of cone [in cm³] = (1/3)π(8²)(y + 7)
volume of cone [in cm³] = (1/3)π(64)(y + 7)
volume of cone [in cm³] = (64π/3)(y + 7)
For the upper cone:
volume of cone = (1/3)πr²h
volume of cone = (1/3)π(4²)y
volume of cone = (16π/3)y
For the frustum:
volume = volume of full cone - volume of upper cone
volume = (64π/3)(y + 7) - (16π/3)y
volume = 64πy/3 + 448π/3 - 16πy/3
volume = 48πy/3 + 448π/3
Now we solve for y:
48πy/3 + 448π/3 = 670.2
50.265y + 469.144 = 670.2
50.265y = 201.056
y = 4.0
Answer: 4.0 cm