Question

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 calculation 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 1

both are equal..becuase if we divide the volume of both we get the differences as one hence are both equal

Answer 2

volume of cylinder=
$\pi \: r { \:}^{2} h$
we can see that volume is directly proportional to height while volume is directly proportional to the square of radius.

Therefore the cylinder with larger radius has more volume, in this case it is cylinder B.

Further if you calculate the volume by using this formula you get-

volume of cylinder A=
$3.14 \times \: 3.5 \times 3.5 \times 14 = 538.51$
volume of cylinder B =
$3.14 \times 7 \times 7 \times 7 = 1077.02$
Therefore it gets verified that cylinder B has more volume than A.

Hope it helps!