Multiple choice

The external and the internal radii of a hollow right circular cylinder of height 15 cm are 6.75 cm and 5.25 cm, respectively. If it is melted to form a solid cylinder of height half of the original cylinder, then the radius of the solid cylinder will be

  1. 6 cm

  2. 6.5 cm

  3. 7 cm

  4. 7.25 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of hollow cylinder = pi * h * (R^2 - r^2) = pi * 15 * (6.75^2 - 5.25^2) = pi * 15 * (6.75 - 5.25)(6.75 + 5.25) = pi * 15 * 1.5 * 12 = 270 * pi. New solid cylinder height = 15/2 = 7.5. pi * r_new^2 * 7.5 = 270 * pi. r_new^2 = 270 / 7.5 = 36. r_new = 6.

AI explanation

The volume of the hollow cylinder is found using the formula pi times height times the difference of the squares of the external and internal radii, which is pi times 15 times (6.75 squared minus 5.25 squared). Using the difference of squares identity, this becomes pi times 15 times 12 times 1.5, giving 270 times pi. Equating this to the volume of the new solid cylinder, pi times radius squared times 7.5, we get radius squared equals 36. Taking the square root gives a radius of 6 cm.

Keep practicing — related questions