Question

Two cylindrical jars have their diameters in the ratio 3 : 1, but height 1 : 3. Then the ratio of their volumes is 

Options

•  1 : 4

• 1 : 3

•  3 : 1

• 2 : 5

Answer 1

Let V₁ and V₂ be the volume of the two cylinders with radius r₁ and height h₁, and radius r₂and height h₂, where `(2r_1)/(2r_2) = 3/1,h_1/h_2 = 1/3`

So,

`V_1 = pir_1^2h_1` ……. (1)

Now,

`V_2 = pir_2^2h_2`   …… (2)

From equation (1) and (2), we have

`V_1/V_2 = (r_1/r_2)^2(h_1/h_2)`

`⇒ V_1/V_2 = ((2r_1)/(2r_2))^2 (h_1/h_2)`

`⇒V_1/V_2 = (3)^2(1/3)=3/1`