Multiple choice

The ratio between the height and radius of the base of a cylinder is 7 : 5. If its volume is 14836.5 cm3, then find its total surface area (take π = 3.14).

  1. 3391.2 cm2

  2. 5391.2 cm2

  3. 4391.2 cm2

  4. 5591.2 cm2
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A Correct answer
Explanation

Given h/r = 7/5, let h = 7x and r = 5x. Volume V = pi * r^2 * h = 3.14 * (5x)^2 * (7x) = 3.14 * 25 * 7 * x^3 = 549.5 * x^3. Setting 549.5 * x^3 = 14836.5 gives x^3 = 27, so x = 3. Thus, r = 15 and h = 21. Total surface area = 2 * pi * r * (r + h) = 2 * 3.14 * 15 * (15 + 21) = 94.2 * 36 = 3391.2.

AI explanation

Using the given ratio, let the radius be 5x and the height be 7x, and apply them to the cylinder volume formula V = πr^2h. Substituting the known values gives 3.14 * (5x)^2 * 7x = 14836.5, which simplifies to 549.5x^3 = 14836.5, making x^3 equal to 27 and x equal to 3. This establishes the radius as 15 cm and the height as 21 cm. Applying the total surface area formula (2πrh + 2πr^2) yields (2 * 3.14 * 15 * 21) + (2 * 3.14 * 15 * 15), resulting in a total surface area of 3391.2 square cm.

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