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

MCQ

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

• 3 times

•  6 times

• 9 times

•  27 times

#### Solution

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.

Concept: Surface Area of Cylinder
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 19 Surface Areas and Volume of a Circular Cylinder
Exercise 19.4 | Q 13 | Page 29

Share