Question
Download Solution PDFVolume of cylinder and cone are in the ratio 25: 16, their height are in the ratio 3: 4. Then ratio of radii of base of cylinder and cone is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Ratio of Volume of Cylinder to Volume of Cone = 25 : 16
Ratio of Height of Cylinder (H1) to Height of Cone (H2) = 3 : 4
Formula Used:
Volume of Cylinder (Vcyl) = πR12H1
Volume of Cone (Vcone) = (1/3)πR22H2
Calculation:
According to the given information:
Vcyl / Vcone = 25 / 16
(πR12H1) / ((1/3)πR22H2) = 25 / 16
Substitute the ratio of heights H1/H2 = 3/4, so H1 = (3/4)H2:
(πR12(3/4)H2) / ((1/3)πR22H2) = 25 / 16
⇒ (3/4)R12 / ((1/3)R22) = 25 / 16
⇒ [(3/4)R12 × 3] / (1 × R22) = 25 / 16
⇒ 9R12 / 4R22 = 25 / 16
⇒ R12 / R22 = (25 / 16) × (4 / 9)
R12 / R22 = 100 / 144
⇒ R1 / R2 = √(100 / 144)
⇒ R1 / R2 = 10 / 12
⇒ R1 / R2 = 5 / 6
∴ The ratio of the radii of the base of the cylinder and the cone is 5 : 6.
Last updated on Feb 11, 2025
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