Work Shown
SA = 2*(base area) + lateral area
SA = 2pi*r^2 + 2pi*r*h
SA = 2pi*r(r + h)
270pi = 2pi*r(r + h)
270 = 2r(r+h)
270/2 = r(r+h)
135 = r(r+h)
135 = 9(9+h)
135/9 = 9+h
15 = 9+h
h = 15-9
h = 6
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Check:
SA = 2*pi*r(r + h)
SA = 2*pi*9(9 + 6)
SA = 270pi
The answer is confirmed.
Answer: B. 6 cm
Step-by-step explanation:
We will work backward from the surface area of the cylinder using the given radius to find the height.
Formula:
SA = 2πrh + 2πr²
Substitute known values:
270π = 2π(9)h + 2π(9)²
Square:
270π = 18πh + 2π(81)
Multiply and subtract 2π(81) from both sides of the equation:
270π - 162π = 18πh
Simplify:
108π = 18πh
Divide both sides of the equation by 18π:
6 = h