Q. 24.0( 150 Votes )

# Diameter of cylinder A is 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area?

Answer :

As cylinder A’s radius is half of radius of cylinder B so its volume will be lesser than that of cylinder B.

Although Cylinder B’s height is half of height of cylinder A but as you know

while calculating the volume we need to square the radius so halving the radius has a greater impact than halving the height.

While calculating surface area, the curved surface area in both will be same and

the total surface area will be greater in the cylinder with the greater radius.

Now, volume of the cylinder = π r^{2} h

Thus, volume of cylinder A = = 539 cub. cm

Volume of cylinder B = = 1078 cub. cm

Also, curved surface area of a cylinder = 2πrh

Curved surface area of cylinder A = = 308 sq. cm

Curved surface area of cylinder B = = 308 sq. cm

Total surface area of Cylinder = 2 π r h + 2 π r^{2}

Total surface area of Cylinder A = 2 × = 385 sq. cm

Total surface area of Cylinder B = 2 × = 616 sq. cm

Hence the surface area of cylinder B is greater.

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