# The circumference of the base of a cylinder open at the top is 132 cm. The sum of radius and height is 41 cm. Find the cost of polishing the outer surface area of the cylinder at the rate of Rs. 10 per square decimeter.

Concept Used: Circumference of the base of the cylinder = 2πr

Outer Surface Area of cylinder = 2πrh

Where r = radius of the cylinder and h = height of the cylinder.

Given: r + h = 41 cm

Circumference of the base of cylinder = 2πr = 132 cm

Explanation:

Let us calculate the value of “r” first,

2πr = 132 cm

r = (3 × 7) cm

r = 21 cm.

Now, let us calculate the height of the cylinder,

r + h = 41

Putting the obtained value of “r” we get,

21 + h = 41

h = 20 cm

Now putting the values of “r” and “h” in the formula of Outer Surface Area of the cylinder we get,

The outer surface area of cylinder = 2πr

The outer surface area of cylinder

The outer surface area of cylinder = 120 × 22

The outer surface area of cylinder = 2640 cm2

Hence, the outer surface area of a cylinder is 2640 cm3.

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