Question : The height of a solid cylinder is 35 cm. The circumference of its base is 37 cm more than the radius. What will be the volume of this cylinder?
Option 1: 4740 cm3
Option 2: 4850 cm3
Option 3: 5390 cm3
Option 4: 4420 cm3
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Correct Answer: 5390 cm 3
Solution : Given: The height of a solid cylinder is 35 cm. The circumference of its base is 37 cm more than the radius. The volume of the cylinder = $\pi r^2h$ Circumference of the circle = $2\pi r$ Where $r$ and $h$ are the radius and height respectively. According to the question, ⇒ $r+37=2\pi r$ ⇒ $37=r\times(2\pi –1)$ ⇒ $37=r\times(2\times\frac{22}{7} –1)$ ⇒ $37=r\times(\frac{44}{7} –1)$ ⇒ $37=r\times(\frac{44–1}{7})$ ⇒ $37=r\times(\frac{37}{7})$ ⇒ $r=7$ cm The volume of the cylinder = $\frac{22}{7} \times7^2\times35$ $=22\times 7\times 35=5390$ cm 3 Hence, the correct answer is 5390 cm 3 .
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