Q 0.2 metres is the height of water in a cylindrical container of radius `r` cm. What is the height of this quantity of water if it is poured into a cylindrical container of radius `4r` cm?

A. 0.125 metres
B. 1.25 cm
C. 12.5 cm
D. 2.35 cm

Correct Answer: B

Explanation:

Step 1: Convert everything into consistent units

Height of water in first cylinder:

h1=0.2 m=20 cmh_1 = 0.2 , ext{m} = 20 , ext{cm}

So, in centimetres:

  • First cylinder: height = 20 cm20 , ext{cm}, radius = r cmr , ext{cm}.

  • Second cylinder: radius = 4r cm4r , ext{cm}.

Step 2: Volume of water in first cylinder

V=πr2h1V = pi r^2 h_1 V=πr2(20)=20πr2 cm3V = pi r^2 (20) = 20pi r^2 , ext{cm}^3

Step 3: Volume in second cylinder

Let the new height be h2 cmh_2 , ext{cm}.

V=π(4r)2h2=π(16r2)h2=16πr2h2V = pi (4r)^2 h_2 = pi (16r^2) h_2 = 16pi r^2 h_2

Step 4: Equating volumes

20πr2=16πr2h2


20=16h220 = 16 h_2 h2=2016=1.25 cmh_2 = frac{20}{16} = 1.25 , ext{cm}

Step 5: Convert back to metres

1.25 cm=0.0125 m1.25 , ext{cm} = 0.0125 , ext{m}

✅ Final Answer:
The height of water in the larger cylinder is 0.0125 metres.

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