Q152
ArithmeticGeometry & Mensuration
If the volume of two solid right circular cylinders are same and their height are in the ratio 1:3, then the ratio of lengths of radii is:
- a.$\sqrt{3} : 1$
- b.$1 : \sqrt{3}$
- c.1 : 3
- d.3 : 1
Answer: (A) $\sqrt{3} : 1$
Equal volumes give $r_1^2 h_1 = r_2^2 h_2$, so $\frac{r_1^2}{r_2^2} = \frac{h_2}{h_1} = 3$. Hence $r_1 : r_2 = \sqrt{3} : 1$; the shorter cylinder must be wider. Option B reverses the ratio, and 3 : 1 forgets the square root.