Question

A cylindrical rod which is $25cm$ long and of $20cm$ in diameter is melted to form another rod of $19cm$ diameter. Find the length of the new rod.

Answer 1

Radius of $C_1=R_1=\frac{20}{2}=10cm$

Height of $C_1=H_1=25cm$

Radius of $C_2=\frac{19}{2}cm$

Height of $C_2=H_2$

Volume of cylinder = $\pi r^{2}h$

According to question

$\pi R_1^2{H}_1=\pi R_2^2{H}_2$

$\pi \left(10{)}^2\right(25)=\pi (\frac{19}{2}{)}^2\left(H_2\right)$

$\frac{10\times 10\times 25\times 2}{19\times 19}=H_2$

$27.7cm=H_2$