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A right cylindrical solid is cut in half to form the figure shown. If the length is 20 cm and the diameter is 8 cm, what is the surface area?
(80π + 160) cm2
(96π + 160) cm2
320π cm2
(320π + 160) cm2
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GPT-5 mini
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Radius = 4 cm (diameter 8), length (height) = 20 cm.
Lateral surface of full cylinder = 2πrh = 2π(4)(20) = 160π, so half the lateral = 80π.
Each end gives two semicircles for the half → total end area = πr^2 = 16π.
Flat cut face = rectangle 20 × 8 = 160.
Total surface area = 80π + 16π + 160 = 96π + 160 cm^2.
Answer: (96π + 160) cm².
Lateral surface of full cylinder = 2πrh = 2π(4)(20) = 160π, so half the lateral = 80π.
Each end gives two semicircles for the half → total end area = πr^2 = 16π.
Flat cut face = rectangle 20 × 8 = 160.
Total surface area = 80π + 16π + 160 = 96π + 160 cm^2.
Answer: (96π + 160) cm².
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