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The second hand on a clock is 8cm long. What is the distance the tip of the second hand travels in 10 minutes? Round your answer to the nearest cm. cm

The second hand on a clock is 8 cm 8 \mathrm{~cm} long.\newlineWhat is the distance the tip of the second hand travels in 1010 minutes?\newlineRound your answer to the nearest cm \mathrm{cm} .\newline□\square cm \mathrm{cm}

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Full solution

Q. The second hand on a clock is 8 cm 8 \mathrm{~cm} long.\newlineWhat is the distance the tip of the second hand travels in 1010 minutes?\newlineRound your answer to the nearest cm \mathrm{cm} .\newline□\square cm \mathrm{cm}
  1. Calculate Circumference Formula: The second hand makes a full circle every minute, so in 1010 minutes, it will make 1010 full circles.
  2. Calculate Radius Length: The circumference of a circle is given by the formula C=2⋅π⋅rC = 2 \cdot \pi \cdot r, where rr is the radius.
  3. Calculate Circumference: The length of the second hand is the radius, which is 88 cm. So, C=2×π×8C = 2 \times \pi \times 8.
  4. Multiply Circumference by Time: Calculate the circumference: C=2×π×8=16πC = 2 \times \pi \times 8 = 16\pi cm.
  5. Approximate Pi: Now, multiply the circumference by the number of circles made in 1010 minutes: 16π cm×10=160π cm16\pi \, \text{cm} \times 10 = 160\pi \, \text{cm}.
  6. Calculate Distance: Use the approximation π≈3.14\pi \approx 3.14 to find the distance: 160×3.14160 \times 3.14 cm.
  7. Round to Nearest cm: Calculate the distance: 160×3.14=502.4160 \times 3.14 = 502.4 cm.
  8. Round to Nearest cm: Calculate the distance: 160×3.14=502.4160 \times 3.14 = 502.4 cm.Round the answer to the nearest cm: 502.4502.4 cm ≈502\approx 502 cm.

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