Question

A copper sphere of 36m diameter is drawn into a cylindrical wire of length 7.29km find ots radius​

Answer 1

✰✰|| To Find ||✰✰

• radius of cylindrical wire

✪|| Solution ||✪

1 km = 1000m

7.29km = 7290m

Diameter of sphere = radius × 2

↬ 36m = radius × 2

↬ radius = 36m/2

↬ radius = 18m

Area of sphere = Area of cylinder

➻ 4πr² = Area of cylinder

➻ 4 × 22/7 × 18m² = Area of cylinder

➻ 88/7 × 324m² = Area of Cylinder

➻ 28,512m²/7 = Area of cylinder

➻ 7,128m² = Area of cylinder

Let, the radius of cylinder be x

Area of cylinder = 7,128m²

⇒ 2πr²h = 7,128m²

⇒ 2 × 22/7 × x² × 7,290m = 7,128m²

⇒ 44/7 × x² = 7,128m²/7,290m

⇒ 44/7 × x² = 7,128m/7,290

⇒ 44 × x² = 7,128m/7,290 × 7

⇒ 44 × x² = 49,896/7,290

⇒ 44 × x² = 6.84

⇒ x² = 6.84 ÷ 44

⇒ x² = 0.15

⇒ x = √0.15

⇒ x = 0.387

The radius of cylindrical wire is 0.387

Answer 2

Answer:

The radius of the cylindrical wire would be 0.298142397m.

Step-by-step explanation and calculation:

We all know that,

1 Km= 1000 m

∴ 7.29 Km= 7290 m

Finding out the radius of the copper sphere:

We know that,

Diameter of the sphere= 2 × Radius of the sphere (r)

⇒ 36m = 2 × r

⇒ r = 18m

Calculation of the wire radius:

∵ The sphere is re-moulded into a cylindrical wire of length of 7.29 Km,

∴ Area of the Cylinder = Area of the Sphere

⇒ 2πr² (radius of the cylinder) × h = 4πr² (radius of the sphere)

Let the radius of the cylindrical wire be x.

⇒ 2 × $\frac{22}{7}$ × x² × 7290 = 4 × $\frac{22}{7}$ × (18)²

⇒ 2 × $\frac{22}{7}$ × x² × 7290 = $\frac{88}{7}$ × 324

⇒ $\frac{44}{7}$ × x² × 7290= $\frac{88}{7}$ × 324

⇒  $\frac{44}{7}$ × x² × 7290= 4073.1428571429

⇒ $\frac{44}{7}$ × x²= $\frac{4073.1428571429}{7290}$

⇒ $\frac{44}{7}$ × x²= 0.5587301587

⇒ x² = $0.5587301587 * \frac{7}{44}$

⇒ x= √0.0888888889

⇒ x= 0.298142397m

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