Mensuration Practice Question based on conversion of shapes

Question of The Day06-12-2021

A copper Spherical ball of diameter 240 m. is melted and molded to form wire of length 4 km. What should be the diameter of Wire?

Answer

Correct Answer : b ) 48 m

Explanation :

According to the question,

The spherical ball has been used to form cylindrical wire.

We know that, Volume of the material would remain same, i.e., Volume of Spherical ball = Volume of Cylindrical wire.

Let the radius of wire be R, radius of ball be r and height of the cylinder be h.

Diameter of Spherical ball = 240 m

Radius of the ball, r = \(240 \over 2\)=120 m

Length of Cylindrical wire = h = 4 km

⇒ h = 4000 m

We know that

Volume of Sphere=\({4 \over 3}πr^3\)

The sphere is melted and recasted into the wire of cylindrical shape

Volume of Cylinder = πr2h

Where ‘r’ and ‘h’ are the radius and height of the cylinder, respectively.

Volume of Spherical ball = Volume of cylindrical wire

⇒\({4 \over 3}πr^3 =πR^2h\)

Substituting the values

\({4 \over 3}π*120*120*120=π*R^2*4000\)

⇒ R² = 576

⇒ R = 24m

Diameter of wire = 2 * 24 m

⇒ 48 m

Hence, (b) is the correct answer.

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