Question

The radius of a wire is decreased to one-third. If volume remains the same, the length will become

Options

• 3 times

•  6 times

• 9 times

•  27 times

Answer 1

Let V₁ and V₂ be the volume of the two cylinders with h₁ and h₂ as their heights:

Let r₁ and r₂ be their base radius.

It is given that

                                               `pi r_1^2 h_1 = pir_2^2 h_2`

`V_1 = V_2 " and " r_2 = 1/3 r_1 ⇒ r_1^2 h_1 = (1/3r_1)^2 h_2`

                                           `⇒h_2 = 9h_1`

Hence, the length will become 9 times.