Question

the radius of a wire is decreased to 1by3 of its previous one if the volume remains same find ratio​

Answer 1

Answer:

We knows that wire is in the shape of a cylinder.

So, volume of wire = \pi r^2hπr

2

h

\pi r^2hπr

2

h = \pi (r/3)^2hπ(r/3)

2

h

\pi r^2hπr

2

h = \pi \frac{r^2}{9} hπ

9

r

2

h

Cancelling π on both sides,

r^2h = \frac{r^2}{9} hr

2

h=

9

r

2

h

9r^2h = r^2h9r

2

h=r

2

h

Now cancelling 'r²' on both sides, we get

9h = h9h=h

So, height is increased by 9 times.

Answer 2

Step-by-step explanation:

volume of wire= πR²H

V(i) initial volume = V(f) final volume

V(i)/V(f) =π R1² *H1/πR2²*H2

--> R1² *H1 = R2²*H2

--> R1² / R2²= H2/H1

R2 = 2/3 R1

R1² / 4/9*R1² = H2/H1

9/4= H2/H1