Question

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

Answer 1

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.