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.
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Answer:
Let r1 and r2 be the respective radii of first and second cylinder.
Diameter of 1st cylinder = 16 cm
Radius = r1 = 16/2 = 8 cm
Diameter of 2nd cylinder = 14 cm
Radius = r2 = 14/2 = 7 cm
Height of 1st cylinder = h1 = 49 cm
Height of 2nd cylinder = h2 = 35 cm
Volume of 1st cylinder = πr1²h
⇒ (22*8*8*49)/7
⇒ 9856 cm³
Volume of 2nd cylinder = πr2²h
⇒ (22*7*7*35)/7
⇒ 5390 cm³
Total volume = 9856 cm³ + 5390 cm³ = 15246 cm³
Let radius of new cylinder be r.
⇒ Volume of 1st and 2nd cylinder = Volume of the new cylinder
⇒ 15246 cm³ = (22*r²*56)/7
⇒ r² = 106722/1232
⇒ r² = 86.625 cm
⇒ r = √86.625
⇒ r = 9.307 cm
⇒ diameter = 9.307*2 = 18.614 cm
So, the diameter of the new cylinder is 18.614 cm.
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