Question

radius of a sphere is 9cm is melted and drawn into wire of diameter 2mm. find the length of wire

Answer 1

Volume of sphere=
$\frac{4}{3} \pi \: {r}^{3}$
$= \frac{4}{3} \times 3.14 \times {9}^{3} \\ = \frac{4}{3} \times 3.14 \times 729 \\ = \frac{9156.24}{3} \\ = 3053.63$
Now,
Volume of cylinder=
$\pi {r}^{2} \times h \\ 9156.24 = 3.14 \times 0.1 \times h \\ h = \frac{9156.24}{3.14 \times 0.1} \\ h = 97200.06 \: cm$

Answer 2

Answer:

Let R = radius of the sphere

Now, R = 9 cm

volume of sphere, V1 = 43πR3 = 43π(9)3 = 972π cm3

volume of sphere, V1 = 43πR3 = 43π93 = 972π cm3

Now, diameter of the wire  = 2 mm = 0.2 cm       [as 1 cm = 10 mm]

radius of the wire, r = 0.1 cm

Let h = length of the wire

volume of cylindrical wire, V2 = πr2h = (0.1)2πh cm3

volume of cylindrical wire, V2 = πr2h = 0.12πh cm3

Since the sphere is melted and recast into wire, so in this case volume of the material remains same.

So, V2 = V1

⇒(0.1)2πh = 972π⇒0.01 h = 972

⇒h = 97200 cm

⇒h = 972 m            [as, 1m = 100 cm]