two solids of right cylindrical shape of 49 centimetre and 35 cm height and their ways diameters are 16 cm and 14 cm respectively both are melting and molded into a single cylinder 56cm high find its base diameter
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Find the volume of the first cylinder:
Radius = Diamater ÷ 2
Radius = 16 ÷ 2 = 8 cm
Height = 49 cm (Given)
Volume = πr²h
Volume = π(8)²(49) = 3136π cm³
Find the volume of the second cylinder:
Radius = Diamater ÷ 2
Radius = 14 ÷ 2 = 7 cm
Height = 35 cm (Given)
Volume = πr²h
Volume = π(7)²(35) = 1715π cm³
Find their total volume:
Total Volume = 1715π + 3136π = 4851π cm³
Find the radius of the new mould:
Volume = πr²h
4851π = πr²(56)
r² = 4851π ÷ 56π
r² = 86.625
r = √86.625
r = 9.3 cm
Find the diameter :
Diameter = radius x 2
Diameter = 9.3 x 2 = 18.6 cm
Answer: The base diameter is 18.6 cm
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