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Question

A cylindrical rod of height 10 m and radius 7m is melted into 7 identical cylindrical pistons of radius 14m and height 514m

Then,

(1) The volume of the cylindrical rod is equal to the sum of the volume of all 7 pistons .

(2) The total surface area of the cylindrical rod is equal to the sum of total surface area of the cylindrical piston.


A

Both I and II are correct

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B

Only I is correct

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C

Only II is correct

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D

None of these

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Solution

The correct option is B

Only I is correct


Volume of the cylindrical rod = πr2h

= 227×7×7×10

= 1540m3

Volume of one cylindrical piston = πr2h

=

22/7×/142×5/14

= 220 m3

Volume of 7 cylindrical pistons = 7 ×220

=1540m3

= Volume of cylindrical rod.

So, statement 1 is correct.

Now,

Total surface area of cylindrical rod = 2πrh+2πr2

2×22/7×/7×10+2×227×7×7

= 440+308

=748m2

Total Surface area of cylindrical piston = 2πrh+2πr2

2×227×/14×5/14+2×227×14×14

=2207+86247

= 88447m2

Total surface area of 7 cylindrical piston

= 7×88447

= 8844m2

So, statement II is wrong.


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