Question
Download Solution PDFA right circular solid cone of radius 3.2 cm and height 7.2 cm is melted and recast into a right circular cylinder of height 9.6 cm. What is the diameter of the base of the cylinder?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFAs we know,
Volume of cone = (1/3) πr2h
Volume of cylinder = πR2H
Radius of cone (r) = 3.2 cm
Height of cone (h) = 7.2 cm
Height of cylinder (H) = 9.6 cm
Radius of cylinder = R
According to the question
πR2H = (1/3) πr2h
⇒ R2 × 9.6 = (1/3) × 3.2 × 3.2 × 7.2
⇒ R2 = (3.2 × 3.2 × 7.2)/(3 × 9.6) = (3.2 × 3.2)/4
⇒ R = √(3.2 × 3.2)/4 = 3.2/2 = 1.6
Diameter of the cylinder = 2 × 1.6 = 3.2
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