Question

a iron sphere of diameter 18 cm is drawn into a wire of diameter 4 mm find the length of the wire​

Answer 1

Answer:

24300 cm

Step-by-step explanation:

Diameter of Sphere = 18 cm

Radius(r) of sphere = diameter /2 = 18/2 = 9 cm

Volume of sphere =\frac{4}{3} \pi r^{3}34πr3

                              =\frac{4}{3} \pi 9^{3}34π93

Diameter of wire = 4 mm

10 mm = 1 cm

So, 1mm = \frac{1}{10}101

4 mm =  \frac{4}{10}=0.4cm104=0.4cm

Radius of wire = Diameter /2 = (0.4)/2= 0.2 cm

Since wire is in the shape of cylinder

So, volume of cylinder = \pi r^{2} hπr2h

Volume of wire = = \pi (0.2)^{2} hπ(0.2)2h

Since we are given that A copper sphere is drawn into a wire

⇒\frac{4}{3} \pi 9^{3}=\pi (0.2)^{2} h34π93=π(0.2)2h

⇒\frac{4}{3}\times 9^{3}= (0.2)^{2} \times h34×93=(0.2)2×h

⇒\frac{4}{3}\times 729 = 0.04\times h34×729=0.04×h

⇒972= 0.04\times h972=0.04×h

⇒\frac{972}{0.04}=  h0.04972= h

⇒24300=  h24300= h

Thus the length of the

Answer 2

Answer:

$\red{\textbf{Answer :-243m}}$

Step-by-step explanation:

$\blue{\texttt{Given :-}}$

$\textsf{Diameter of sphere=18cm}$

$\textsf{Radius=}$

$\Large\frac{18}{2}$

$\textsf{= 9cm}$

$\textsf{diameter of wire= 4 mm}$

$\textsf{radius =2mm=0.2cm}$

$\red{\textbf{Volume of Sphere = Volume of wire(cylinder)}}$

$\Large\frac{4}{3} \pi \: {r}^{3} = \pi \: {r}^{2} h$

$\Large\frac{4}{3} {9}^{3} = 0. {2}^{2} h$

$\textsf{h=24300cm =243 m}$

$\textsf{so,the length of the wire is 243 m}$

$\green{\textbf{More information :-}}$

• The volume of a sphere is 2/3 of the volume of a cylinder with same radius, and height equal to the diameter.

• The volume V of a sphere is four-thirds times pi times the radius cubed.

$V = \LARGE\frac{4}{3} \pi \: {r}^{3}$