Question

Two solids of right cylindrical shape are 49 cm and 35 cm high and their base diameters are 16 cm , 14 cm respectively .Both are melted and moulded into a single cylinder , 56 cm high. Find its base diameter.

Answer 1

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Answer 2

According to question

Radius of first cylinder   R1 = 16/2 = 8 Cm
Height of first cylinder     H1 = 49 Cm

So Volume     V1 = pi R1^2 H1
                            = pi * 64 * 49

Similarly
 Radius of second cylinder    R2 = 14/2 = 7 Cm
Also  Height                           H2 = 35 Cm

So  Volume     V2 = pi R2^2 H2
                              = pi * 49 * 35

When Moulded    Total volume    V = V1 + V2
                                                    V = pi [ 64 * 49 + 49 * 35 ]

Height of New cylinder   H = 56 Cm

Let radius be R

So      V = pi R^2 H
          Pi [ 64 * 49 + 49 * 35 ] = pi R^2 * 56
             R = 9.30 Cm
Thus Diameter = 18.60 Cm