Question

the diameter of a metallic sphere is 6 cm . it is melted and drawn into wire of diameter 0.2 cm then find the length of wire​

Answer 1

Answer:

Step-by-step explanation:

Since the sphere is melted to form wire, they will have the same volume.

Volume of sphere = (4/3)*π*r³

Volume of cylinder = π r²h

According to the question,

(4/3)*π*r³= π r²h

37.68 = 0.314 * h

h= 37.68/ 0.314

= 120 CM

length of wire = 120 cm

Answer 2

Step-by-step explanation:

Answer:-

\red{\bigstar}★ Length of the wire is \large\leadsto\boxed{\tt\green{3600 \: cm or 36 \: m}}⇝

3600cmor36m

• Given:-

Diameter of metallic sphere = 6 cm

Diameter of wire = 0.2 cm

• To Find:-

Length of the wire

• Solution:-

Given that,

Diameter of metallic sphere is 6 cm.

Hence,

Radius of the metallic sphere = d/2

➠ 6/2

➠ 3 cm

Also,

Diameter of the wire is 0.2 cm

Therefore,

Radius of cylindrical wire = d/2

➠ 0.2/2

➠ 0.1 cm

Now, the metallic sphere is melted into cylindrical wire.

Hence,

★ Volume of sphere = Volume of Cylinder

\pink{\bigstar}★ \large\underline{\boxed{\bf\green{\dfrac{4}{3} \pi r^{3} = \pi r^2 h}}}

3

4

πr

3

=πr

2

h

• Substituting in the Formula:-

➠ \sf \dfrac{4}{3} \times \pi \times (3)^3 = \pi \times (0.1)^2 \times h

3

4

×π×(3)

3

=π×(0.1)

2

×h

➠ \sf \dfrac{4}{3} \times \pi \times 27 = \pi \times 0.01 \times h

3

4

×π×27=π×0.01×h

➠ \sf 4 \times \pi \times 9 = \times 0.01 \times h4×π×9=×0.01×h

➠ \sf 36 \: \pi = \pi \times 0.01 \times h36π=π×0.01×h

➠ \sf h = \dfrac{36 \: \pi}{0.01 \: \pi}h=

0.01π

36π

➠ \sf h = \dfrac{36}{0.01}h=

0.01

36

➠ \bf h = 3600h=3600

★ \large{\bf\purple{h = 3600 \: cm \: or \: 36 \: m}}h=3600cmor36m

Therefore, length of the wire is 3600 cm or 36m.