Question

A copper sphere of diameter 18 cm is drawn into a wire of diameter 4mm. find the length of the wire.

Answer 1

volume of sphere = volume of cylindrical wire

4/3 π R^3 = π r^2 h

4 × 90^3 / 3 = 2^2 × h

90 × 90 × 90 /3 = h

h = 243 cm

Answer 2

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 =$\frac{4}{3} \pi r^{3}$

                              =$\frac{4}{3} \pi 9^{3}$

Diameter of wire = 4 mm

10 mm = 1 cm

So, 1mm = $\frac{1}{10}$

4 mm =  $\frac{4}{10}=0.4cm$

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

Since wire is in the shape of cylinder

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

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

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

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

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

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

⇒$972= 0.04\times h$

⇒$\frac{972}{0.04}=  h$

⇒$24300=  h$

Thus the length of the wire is 24300 cm