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
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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