Question : The sum of the curved surface area and the total surface area of a solid cylinder is 2068 cm2. If the radius of its base is 7 cm, then what is the volume of this cylinder? (use $\pi=\frac{22}{7}$)
Option 1: 2060 cm3
Option 2: 2480 cm3
Option 3: 3080 cm3
Option 4: 2760 cm3
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Correct Answer: 3080 cm 3
Solution : Given: The sum of the curved surface area and the total surface area of a solid cylinder is 2068 cm 2 . The radius of its base is 7 cm. Volume of the cylinder $= \pi r^2 h$ The curved surface area of the cylinder $= 2 \pi r h$ Total surface area of the cylinder $= 2\pi r (h+r)$ According to the question, $2068 = 2\pi r h + 2\pi r (r+h)$ ⇒ $2068 = 2 \pi r (h+r+h)$ ⇒ $1034 = \frac{22}{7} \times 7 \times (7+2h)$ ⇒ $47= 7+2h$ ⇒ $40= 2h$ ⇒ $h= 20$ cm The volume of the cylinder $=\frac{22}{7} \times 7^2\times 20=22 \times 7 \times 20 = 3080$ cm 3 Hence, the correct answer is 3080 cm 3 .
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