Question

If the radius and height of a cylinder are in the ratio $5:7$ and its volume is $550c{m}^3$, then its radius is equal to $(Take\pi =\frac{22}{7})$

• A. $6$ cm
• B. $7$ cm
• C. $5$ cm
• D. $10$ cm

Answer 1

Answer: (C)

$5$ cm

Given, volume of a cylinder $=\pi r^{2}h=550$ ${cm}^3$

Also, given, $\frac{r}{h}=\frac{5}{7}$

$\therefore h=\frac{7r}{5}$

Given, $\pi r^{2}h=550$

$\therefore \pi r^2\times \frac{7\times r}{5}=550$

$⟹7\pi r^3=550\times 5$

$⟹r^3=\frac{550\times 5}{7\times \frac{22}{7}}$

$⟹r^3=125$

$⟹r=\sqrt[3]{3125}$

$\therefore r=5$

Thus, the radius of the cylinder is $5$ cm.