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Answer:
(320 +130π) cm²
Step-by-step explanation:
The perimeter of the base will be the sum of two radii and the arc length of a quarter circle:
P = 2r +r(π/2) = r(2+π/2)
For a radius of 10 cm, the perimeter of the base is ...
P = (10 cm)(2+π/2) = (20+5π) cm
The lateral area of the quarter-cylinder is the product of this perimeter and the height:
LA = Ph = ((20 +5π) cm)(16 cm) = (320 +80π) cm²
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The total base area is the area of a half-circle of radius 10 cm, so is ...
BA = 1/2πr² = (1/2)π(10 cm)² = 50π cm²
The total surface area is the sum of the base area and the lateral area:
SA = BA +LA = (50π +(320 +80π)) cm² = (320 +130π) cm²
