Multiple choice

A cylinder of circumference $ 8$ cm and length $21$cm rolls without sliding for $\displaystyle 4\frac{1}{2}$ seconds at the rate of $ 9 $ complete rounds per second. Find the area covered by the cylinder in $\displaystyle 4\frac{1}{2}$ seconds.

  1. $6104$ $\displaystyle cm^{2}$ Area covered by the cylinder in 1 round $= $ its curved surface area.
  2. $6804$ $\displaystyle cm^{2}$ Area covered by the cylinder in 1 round $= $ its curved surface area.
  3. $6404$ $\displaystyle cm^{2}$ Area covered by the cylinder in 1 round $= $ its curved surface area.
  4. $6204$  $\displaystyle cm^{2}$ Area covered by the cylinder in 1 round $= $ its curved surface area.
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B Correct answer
Explanation

The circumference is 8 cm and length is 21 cm. In one round, the area covered is the curved surface area: 8 * 21 = 168 cm^2. The cylinder rolls for 4.5 seconds at 9 rounds per second, totaling 40.5 rounds. Total area = 40.5 * 168 = 6804 cm^2.

AI explanation

The total rounds made are 9 rounds per second multiplied by 4.5 seconds, giving 40.5 rounds. The curved surface area is the circumference multiplied by the length, calculated as 8 cm * 21 cm, which is 168 sq cm. Multiplying this area by the 40.5 rounds gives a total covered area of 6804 sq cm.

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