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The curved surface area of a right circular cylinder is 440 cm² and its radius is 7 cm. Find its height. (Use pi = 22/7)
10 cm
14 cm
7 cm
20 cm
10 cm
Use the fact that 2 × (22/7) × 7 cancels the 7, reducing the equation to 44 × h = 440. Simply divide 440 by 44 to get the height directly.
Curved surface area of a right circular cylinder = 440 cm², Radius (r) = 7 cm, π = 22/7
CSA=2πrh
Use the fact that 2 × (22/7) × 7 cancels the 7, reducing the equation to 44 × h = 440. Simply divide 440 by 44 to get the height directly.
Students often use the Total Surface Area formula 2πr(r+h) instead of the Curved Surface Area formula, leading to an incorrect result.
Identify given variables
We are given the curved surface area CSA=440 cm2 and radius r=7 cm.
CSA=440,r=7
Apply formula
Substitute the known values into the curved surface area formula CSA=2πrh.
440=2×722×7×h
Solve for h
Cancel 7 in the numerator and denominator, then solve for h by dividing 440 by 44.
440=44×h⟹h=44440=10
A is correct because substituting the given values into the formula yields a height of 10 cm.
This concept of isolating one variable from a geometric formula is essential for solving problems in 3D geometry and fluid mechanics volume calculations.
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