Question

A sphere of radius 6cm is moulded intro a thin cylindrical wire of length 32cm.Calculate the radius of the wire in si units

Answer 1

Answer:

Mass of sphere,M= (4/3) pi R^3d= mass of wire = pi r^2 l d. …….(1)

d is density of metal.

R=12 cm.

r= 16 cm. (!)

l is length of the wire to be found.

Using these values in equation (1),

l = [4 (12)^3]/[3 (16)^2]=9 cm

Explanation:

Answer 2

Answer :

The radius of the wire is 9cm

Given :

• A sphere of radius 6cm is moulded into a thin cylindrical wire of length 32cm.

To Find :

• The radius of the cylindrical wire.

Formula to be used :

Volume of a cylinder ,

$\rm \dashrightarrow \pi r^{2} h$

Volume is of a sphere ,

$\rm \dashrightarrow \dfrac{4}{3}\pi r^{3}$

Solution :

Given,

The radius of the sphere is , r = 6cm

The length of the cylinder is ,

h = 32cm

Therefore , according to question :

$\rm \implies \dfrac{4}{3}\pi r_{1} ^{3} = \pi r_{2} ^{2} h \\\\ \rm \implies \dfrac{4}{3} \times (6)^{3} = r_{2} \times 32 \\\\ \implies \rm r_2 = \dfrac{4\times 6\times 6 \times6 }{3 \times 32}\\\\ \rm \implies r_{2} = 9$

Thus , required radius of the cylindrical wire is 9cm