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
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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