Question

A solid cylinder of diameter 100 mm and height 50 mm is forged between two frictionless flat dies to a height of 25 mm. The percentage change in diameter is

• A. 0
• B. 2.07
• C. 20.7
• D. 41.4

Answer 1

The correct option is D 41.4

Since volume remains constant

$\therefore V_1=V_2$

$\frac{\pi }{4}{d}_1^2{h}_1=\frac{\pi }{4}{d}_2^2{h}_2$

$\left(100{)}^2\right(50)=d_2^2(25)$

or $d_2=141.4m$

$\therefore \%\text{change}=\frac{d_2-d_1}{d_1}\times 100$

$=\left(\frac{141.4-100}{100}\right)\times 100$

$=41.4\%$