Cone-to-cylinder water transfer with π = 22/7: A cone of radius 3.5 cm and height 27 cm is full of water. The water is poured into a cylinder of radius 2.1 cm. Find the height (in cm) of water in the cylinder. (Use π = 22/7.)
Aptitude
Area
Difficulty: Easy
Choose an option
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A50 cm
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B25 cm
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C12.5 cm
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D37.5 cm
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E30 cm
Answer
Correct Answer: 25 cm
Explanation
Introduction / Context:Volumes are conserved when a fluid is transferred. Set the cone’s volume equal to the cylinder’s volume and solve for the cylinder’s height using π = 22/7 for tidy arithmetic with the given radii.
Given Data / Assumptions:
- Cone: r = 3.5 cm, h = 27 cm, V_cone = (1/3)πr^2h.
- Cylinder: R = 2.1 cm, height H unknown, V_cyl = πR^2H.
- π = 22/7.
Concept / Approach:Equate (1/3)πr^2h = πR^2H and cancel π. Compute numerically with exact fractions to avoid rounding.
Step-by-Step Solution:
V_cone = (1/3)*(22/7)*(3.5)^2*27 = (1/3)*(22/7)*12.25*27 = 346.5 cm^3.Cylinder cross-sectional factor: (22/7)*(2.1)^2 = (22/7)*4.41 = 13.86.Set 346.5 = 13.86 * H ⇒ H = 346.5 / 13.86 = 25 cm.Verification / Alternative check:Reverse: 13.86 * 25 = 346.5, matches the cone’s volume.
Why Other Options Are Wrong:12.5, 37.5, 50, 30 do not satisfy volume equality with the given radii.
Common Pitfalls:Forgetting the 1/3 in the cone volume or using diameter instead of radius.
Final Answer:25 cm