Multiple choice

The volume of iron used in making a pipe of height 14 cm is 748 cm3. Find the thickness of the pipe if the external radius of the pipe is 9 cm.

  1. 8 cm

  2. 1 cm

  3. 17 cm

  4. 6 cm

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of a hollow pipe is pi * h * (R^2 - r^2). Given V=748, h=14, R=9. 748 = (22/7) * 14 * (81 - r^2). 748 = 44 * (81 - r^2). 17 = 81 - r^2. r^2 = 64, so r = 8. Thickness = R - r = 9 - 8 = 1 cm.

AI explanation

The volume of the pipe is found using the formula for the volume of a hollow cylinder, pi times height times external radius squared minus internal radius squared. Substituting the known values gives 748 equals 22 over 7 times 14 times 9 squared minus internal radius squared, which simplifies to 17 equals 81 minus internal radius squared. Solving this gives the internal radius squared as 64, so the internal radius is 8 centimeters. The thickness is the external radius minus the internal radius, which is 9 minus 8, equaling 1 centimeter. The thickness of the pipe is 1 centimeter.

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