Multiple choice

A right circular cylinder is formed. A = Sum of total surface area and the area of the two bases B = Curved surface area of this cylinder If A : B = 3 : 2 and the volume of cylinder is 4312 cm3, then what is the sum of area (in cm2) of the two bases of this cylinder?

  1. 154

  2. 308

  3. 462

  4. 616
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let r be radius, h be height. A = (2*pi*r^2 + 2*pi*r*h) + 2*pi*r^2 = 4*pi*r^2 + 2*pi*r*h. B = 2*pi*r*h. A/B = (4*pi*r^2 + 2*pi*r*h) / (2*pi*r*h) = 3/2. 2*pi*r^2 / (pi*r*h) + 1 = 1.5 => 2r/h = 0.5 => h = 4r. Volume = pi*r^2*h = pi*r^2*(4r) = 4*pi*r^3 = 4312. r^3 = 4312 / (4 * 22/7) = 1078 * 7 / 22 = 49 * 7 = 343. r = 7. Area of two bases = 2 * pi * r^2 = 2 * 22/7 * 49 = 308.

AI explanation

Value A is the total surface area plus the two base areas, which means A is actually the curved surface area plus four base areas, so A divided by B equals 3 divided by 2. Simplifying this shows the curved surface area equals two times the sum of the base areas, meaning the total surface area is three times the base area sum. Using the cylinder volume formula, 4312 equals pi*(r)^2*(14), so the base area pi*(r)^2 is 154 and the sum of the two bases is 308 cm2.

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