Two cylindrical pots contain the same amount of water. If their diamet

1.	Two cylindrical pots contain the same amount of water. If their diameter are in the ratio 2 : 3, then what is the ratio of their heights?
Answer» Let r₁, h₁ and r₂, h₂ be the radii and height of the two cylinders respectively. Then \(πr^2_1h_1 = πr^2_2h_2 ⇒\frac{h_1}{h_2}=\frac{r^2_2}{r^2_1}=\big(\frac{r_2}{r_1}\big)^2=\bigg(\frac{\frac32}{\frac22}\bigg)^2=\frac94.\)

Two cylindrical pots contain the same amount of water. If their diameter are in the ratio 2 : 3, then what is the ratio of their heights?

Answer»

Let r₁, h₁ and r₂, h₂ be the radii and height of the two cylinders respectively. Then

\(πr^2_1h_1 = πr^2_2h_2 ⇒\frac{h_1}{h_2}=\frac{r^2_2}{r^2_1}=\big(\frac{r_2}{r_1}\big)^2=\bigg(\frac{\frac32}{\frac22}\bigg)^2=\frac94.\)