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If the ratio of per-unit cost of painting the curved surface to the per-unit cost of painting the plane surface of a cylinder is 3: 2 while the ratio of the total cost of painting the curved surface to that of both the plane surfaces is 9: 8, then the height of the cylinder is what percent of its radius?

If the ratio of per-unit cost of painting the curved surface to the per-unit cost of painting the plane surface of a cylinder is 3: 2 while the ratio of the total cost of painting the curved surface to that of both the plane surfaces is 9: 8, then the height of the cylinder is what percent of its radius? Correct Answer 75%

GIVEN:

Ratio of per unit cost of painting the CSA to per-unit cost of painting the PSA of a cylinder = 3: 2 ratio of the total cost of painting the CSA to PSA = 9: 8

CONCEPT:

h : r can be found from the given data.

FORMULA USED:

Curved surface area of cylinder = 2πrh

Plane surface area of cylinder = 2πr2

CALCULATION:

Let per unit cost of painting the curved surface and plane surface is ‘3x’ and ‘2x’ respectively.

According to the question:

(2πrh × 3x): (2πr2 × 2x) = 9: 8

⇒ h : r = 3/4

∴ Required per cent = (3/4) × 100 = 75%

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