Question

The base radius of an iron cylinder is 14 cm and its height is 28 cm. It is melted and recast into a cylinder of base radius 20 cm. What is the height of this cylinder of base radius 20 cm?

• A. 13.72 cm
• B. 14 cm
• C. 15 cm
• D. 14.72 cm

Answer 1

The correct option is A

13.72 cm

Base radius of first cylinder $\left(r_1\right)$ = 14 cm

Height of first cylinder $\left(h_1\right)$ = 28 cm

Base radius of second cylinder $\left(r_2\right)$ = 20 cm

Height of second cylinder $\left(h_2\right)$ = ?

Volume of second iron cylinder = Volume of first iron cylinder

$\pi r_2^2{h}_2=\pi r_1^2{h}_1$

$\text{/}\pi (20{)}^2{h}_2=\text{/}\pi (14{)}^2\times 28$

$h_2=\frac{14\times 14\times 28}{20\times 20}=\frac{343}{25}=13.72cm$

Hence the height of the recast cylinder = 13.72 cm