Multiple choice

The ratio of the total surface area to the lateral surface area of a cylindrical vessel is 27 : 20. The radius of the cylindrical vessel is 39 cm less than the height of the cylindrical vessel. The cylindrical vessel is filled up to 75% of its capacity with juice. The total juice from the cylindrical vessel is transferred into N conical vessels whose radius is 7 cm and height is 9 cm. What is the value of N?

  1. 125

  2. 135

  3. 164

  4. 165

  5. 170
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total surface area of cylinder is 2*pi*r*(r+h) and lateral is 2*pi*r*h. Ratio (r+h)/h = 27/20. Given r = h - 39, substitute to get (2h-39)/h = 27/20. 40h - 780 = 27h, so 13h = 780, h = 60, r = 21. Volume = pi * 21^2 * 60. Juice = 0.75 * Volume. N = (0.75 * pi * 21^2 * 60) / (1/3 * pi * 7^2 * 9). N = (0.75 * 441 * 60) / (49 * 3) = 11907 / 147 = 135.

AI explanation

The ratio of the total surface area to the lateral surface area of the cylinder is 2*pi*r*(r+h) divided by 2*pi*r*h, which simplifies to (r+h) divided by h, and setting this equal to 27 divided by 20 gives 20r plus 20h equals 27h, meaning 20r equals 7h. Given that the radius is 39 cm less than the height, substituting r equals h minus 39 gives 20h minus 780 equals 7h, so the height is 60 cm and the radius is 21 cm. The volume of juice is 75 percent of the cylinder's volume, which is 0.75 times pi times 21 squared times 60, resulting in 19845*pi cubic cm. The volume of one conical vessel is one third times pi times 7 squared times 9, which equals 147*pi cubic cm, so the number of vessels N is 19845 divided by 147, which equals 135.

Keep practicing — related questions