Question : The ratio of the volume of two cylinders is 27 : 25 and the ratio of their heights is 3 : 4. If the area of the base of the second cylinder is 3850 cm2, then what will be the radius of the first cylinder?
Option 1: 42 cm
Option 2: 56 cm
Option 3: 63 cm
Option 4: 34 cm
Correct Answer: 42 cm
Solution :
According to the question
Let the volume of two cylinders = $27x$ and $25x$
Height of cylinders = $3h$ and $4h$
⇒ The volume of the second cylinder = 3850 × 4$h$
Let the radius of the first cylinder be r
⇒ The base area of the first cylinder = ${\pi r^{2}}$
⇒ The volume of the first cylinder = ${\pi r^{2}} × 3 h$
Now, according to the question
⇒ $\frac{ {\pi r^{2}} × 3 h}{3850 × 4h}= \frac{27}{25}$
⇒ $\frac{22 ×r^2×3}{7× 3850 × 4}= \frac{27}{25}$
⇒ $r^2 = 1764$
⇒ r = 42 cm
Hence, the correct answer is 42 cm.
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