Question

A cylindrical gas container is closed at the top and open at the bottom ; if the iron plate of the top is 5/4 times as thick as the plate forming the cylindrical sides. The ratio of the radius to the height of the cylinder using minimum material for the same capacity is –

• A. 2/3
• B. ½
• C. 4/5
• D. ) 1/3

Answer 1

Answer: (C)

4/5

Answer 2

V = pr²h

If k be the thickness of the sides then that of the top will be (5/4)k.

\ S = (2prh) k + (pr²) (5/4) k ('S' is volume of material used)

or S = 2prk . $\frac { \mathrm { V } } { \pi \mathrm { r } ^ { 2 } }$ + $\frac { 5 } { 4 }$pr²k = k

\ $\frac { \mathrm { dS } } { \mathrm { dr } }$ = k , \ r³ = 4V/5p

= k = p $\left( 5 \pi + \frac { 5 } { 2 } \right)$ = + ive

When r³ = 4v/5p or 5pr³ = 4pr²h

\ r/h = 4/5.