The radius of a cylinder is doubled and the hieght remains the same. The ratio between the volumes of the new cylinder and the orignal cylinder is a) 1:2b) 3:1c) 4:1d) 1:8

The radius of a cylinder is doubled and the hieght remains the same. T

1.	The radius of a cylinder is doubled and the hieght remains the same. The ratio between the volumes of the new cylinder and the orignal cylinder is a) 1:2b) 3:1c) 4:1d) 1:8
Answer» The radius of a cylinder is doubledheight remains the sameTo Find:-The ratio between the volumes of the new cylinder and the original cylinder.Solution:-Let the radius of original cylinder be r and HEIGHT be h.For original cylinder,Radius = rHeight = hWe know,Curved Surface AREA of the cylinder = 2πrh.Hence,CSA of original cylinder = 2πrh.For new cylinder,radius is doubled.Hence,Radius = 2R Height = hCurved Surface Area of the new cylinder is as follows:-CSA = 2π × 2rh⇒ CSA = 4πrhNow,Ratio between the Curved Surface Area of original cylinder and the new cylinder is as follows:-• Ratio = CSA of original cylinder : CSA of new cylinder⇒ Ratio = 2πrh : 4πrhHere πrh cancels out for both numerator and denominatorHence,Ratio = 2 : 4⇒ Ratio = 1 : 2∴ Ratio between the Curved Surface Area of original cylinder and the new cylinder US 1 : 2Hence, Option (a) 1 : 2 is the correct answer.________________________________Other formulas related to cylinder:Volume of cylinder = πr²h cu.unitsTotal Surface Area = 2πr(r + h) sq.units________________________________