Math, asked by nadhanasrin2692, 11 months ago

A solid metal sphere of 6 cm diameter is melted and a cylinder of thickness 2 cm is prepared.Find the diameter of the cylinder.

Answers

Answered by Anonymous
6

Answer:

The diameter of the cylinder prepared by melting of the sphere is 6√2cm

Step-by-step explanation:

Given ,

• the diameter of a solid metal sphere, d = 6cm

so the radius of the sphere , r = 3cm

Now the volume of the solid sphere is

   v_{sphere} = \frac{4}{3}  \pi {r}^{3}  \\   \implies v_{sphere}  =  \frac{4}{3}  \pi \times  {3}^{3}  \\  \implies v_{sphere}  = 36 \pi \: cm

Again , in the question we are given that

The solid sphere is melted to form a cylinder of thickness 2cm ,

Therefore ,

Volume of solid sphere = Volume of cylinder

v_{sphere}  = v_{cylinder}  \\ \implies 36 \pi \: cm ^{3}   =  \pi (r _{2})  {}^{2} h \: (where \: h \: is \: the \: thikness) \\  \implies36 \pi \: cm {}^{3}  =  \pi (r_{2} )^{2}  \times 2cm \\  \implies 18cm {}^{2}  =  ({r_{2} })^{2}  \\  \implies (r_{2} )^{2}  =   ({3 \sqrt{2}cm )}^{2}  \\  \implies r_{2} = 3 \sqrt{2}

Thus the radius of the prepared cylinder is 3√2cm

So , the diameter of the cylinder is 2×radius = 6√2cm

Answered by pandaXop
1

Diameter = 62 cm

Step-by-step explanation:

Given:

  • Diameter of solid metal sphere is 6 cm.
  • Height or thickness of Cylinder is 2 cm.

To Find:

  • What is the diameter of the cylinder?

Solution: We know that Radius = Diameter/2

Radius of sphere = 6/2 = 3 cm.

Volume of Sphere =

 \frac{4}{3} \pi \: r ^{3}

\small\implies{\sf } 4/3π(3)³

\small\implies{\sf } 4/3π27cm³

\small\implies{\sf } 36π cm³

Since, The sphere is melted to form a cylinder therefore, Volume of Sphere = Volume of Cylinder.

Volume of Cylinder = πr²h

\small\implies{\sf } πr²2

\small\implies{\sf } 2πr²

A/q

\small\implies{\sf } 36π cm³ = 2πr cm²

\small\implies{\sf } 36π cm³/2πr cm² = 0

\small\implies{\sf } 18π cm

\small\implies{\sf } 32 cm

Hence, The radius of Cylinder is 32 cm therefore its diameter will be 2 x 32 = 62 cm

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