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A cylindrical rod has an outer curved surface area of 4400 cm2. If the length of the rod is 10 cm, then the outer radius (in cm) of the rod is: (Take π=22/7)
50
70
80
140
70
Observe the expression 4400=2×(22/7)×r×10. Simplifying 4400=(440/7)×r, it is clear r=4400×7/440, which is 10×7=70.
Outer curved surface area of the cylinder (CSA) = 4400 cm², length (height) of the rod h = 10 cm, value of π = 22/7.
CSA=2×π×r×h
Observe the expression 4400=2×(22/7)×r×10. Simplifying 4400=(440/7)×r, it is clear r=4400×7/440, which is 10×7=70.
Students often confuse the curved surface area with the total surface area, which includes the area of the two circular bases (2×π×r2).
State the formula for Curved Surface Area
The formula for the curved surface area (CSA) of a cylinder with radius r and height h is given by:
CSA=2πrh
Substitute the given values
Plug in the given values CSA=4400, h=10, and π=22/7 into the formula:
4400=2×722×r×10
Solve for the radius r
Simplify the equation: 4400=7440×r. Multiplying both sides by 7/440 gives r=4404400×7.
r=10×7=70
B is correct because solving the equation 4400=2×(22/7)×r×10 yields r=70.
This concept of lateral surface area is frequently used in 3D geometry problems involving pipes, pillars, and wire dimensions in physics.
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