2. 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?

Answers (1)

Given the diameter of cylinder A = 7cm and the height = 14cm.

Also, the diameter of cylinder B = 14cm and height = 7cm.

We can easily suggest whose volume is greater without doing any calculations:

As volume is directly proportional to the square of the radius of cylinder and directly proportional to the height of the cylinder hence 

B has more Volume as compared to A because B has a larger diameter.

Verifying:

Volume of A :  \pi\times r^2\times height = \pi\times (\frac{7cm}{2})^2\times 14cm =539cm^3

and Volume of B :  \pi\times r^2\times height = \pi\times (\frac{14cm}{2})^2\times 7cm =1,078cm^3.

Hence clearly we can see that the volume of cylinder B is greater than the volume of cylinder A.

The cylinder B has surface area of  = 2\times \pi\times r(r+h) = 2\times \pi\times \frac{14cm}{2}(\frac{14}{2}+7) = 616cm^2.

and the surface area of cylinder A = 2\times \pi\times r(r+h) = 2\times \pi\times \frac{7cm}{2}\times (\frac{7}{2}+14) = 385cm^2.

The cylinder with greater volume also has greater surface area.

 

 

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