two right circular cylinders of equal volume have their heights in the ratio4:9. find the ratio of their radii. If radius of one right circular cylinder is 4 cm then what is radius of other right circular cylinder
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Given that,
Volume of 1st cyl. = Volume of the 2nd one
⇒ (V_1st)/(V_2nd) = 1:1
∵ Volume of a right circular cylinder = πr²h
⇒ (πr²h)/(πR²H) = 1/1
⇒ (4πr²)/(9πR²) = 1/1
⇒ r²/R² = 9/4
⇒ r/R = 3:2.
Now, let the radius of the second cylinder be = x
∴ x/4 = 3/2
⇒ 2x = 12
⇒ x = 6 cm.
If 4 cm is greater,
4/x = 3/2
⇒ x = 8/3 = 2.66 cm.
∴ The ratio of their radii is 3:2 and if one of the cylinder's raidus is 4 cm, then the second's is of 6 cm or 2.66 cm.
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