Question : The ratio of the volume of the first and second cylinders is 32 : 9 and the ratio of their heights is 8 : 9. If the area of the base of the second cylinder is 616 cm2, then what will be the radius of the first cylinder?
Option 1: 24 cm
Option 2: 20 cm
Option 3: 28 cm
Option 4: 36 cm
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Correct Answer: 28 cm
Solution :
Volume of cylinder = $\pi r^2h$
The volume of the cylinder can be written as $32y$ and $9y$
The height of the cylinder can be written as $8h$ and $9h$
Since we know that the volume of the cylinder = Area of the base × height
⇒ Volume of second cylinder = $616 \times 9h$
Let the radius of the first cylinder be r
⇒ Base area of first cylinder = $\pi r^2$
Volume of first cylinder = $\pi r^2 \times 8h$
Their ratios can be written as
$⇒\frac{ 616 \times 9h}{(\pi r^2 \times 8h)} = \frac{9}{32}$
$⇒\frac{(22r^2 \times 8)}{(616 \times 9 \times 7)} = \frac{32}{9}$
⇒ $r^2 = \frac{(616 \times 9 \times 32 \times 7)}{(9 \times 22 \times 8)}$
⇒ $r^2$ = 784
⇒ $r$ = 28
∴ The radius of the first cylinder is 28 cm.
Hence, the correct answer is 28 cm.
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