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Curved surface of a cylinder is to be painted with Red color while its plane surfaces are to be painted with Blue color. If cost of painting with Red and Blue color is Rs. 14 per cm2 and Rs. 10 per cm2‑ respectively and total cost of painting with both the colors is same, then what is the ratio of radius and height of the cylinder?

Curved surface of a cylinder is to be painted with Red color while its plane surfaces are to be painted with Blue color. If cost of painting with Red and Blue color is Rs. 14 per cm2 and Rs. 10 per cm2‑ respectively and total cost of painting with both the colors is same, then what is the ratio of radius and height of the cylinder? Correct Answer 7 : 5

GIVEN:

Cost of painting with Red and Blue color is Rs. 14 and Rs. 10 respectively.

CONCEPT:

Costs for painting CSA and PSA are be equated.

FORMULA USED:

Curved surface area of cylinder = 2πrh

Plane surface area of cylinder = 2πr2

CALCULATION:

Let radius and height of the cylinder is ‘r’ and ‘h’ respectively.

According to the question:

2πrh × 14 = 2πr2 × 10

⇒ 14h = 10r

⇒ r : h = 7 : 5

∴ Required ratio of radius and height is 7 : 5

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