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50 students of class X planned a visit to an old age home and to spend the whole day with its inmates. Each one prepared a cylindrical flower vase using cardboard to gift the inmates. The radius of cylinder is $4.2 cm$ and the height is $11.2 cm$ . What is the amount spent for purchasing the cardboard at the rate of Rs.20 per $100 cm 2 ?$

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Rs.3511.20

Rs.3501.20

Rs.3511

Rs.4511.20

answer is A.

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Detailed Solution

Given that the numbers of students are 50, the radius of a cylindrical flower vase is

4.2 cm

, the height is

11.2 cm

and the rate of cardboard is Rs.20 per

100 cm 2

.
We have the following formula,
The surface area of the cylindrical base

= 2 π r h + π r 2

The surface area of the cylindrical base will be the sum of the curved surface area of the cylindrical flower base and the area of the base. Then,
r

= 4.2 c m

= 11.2 c m

The surface area of the cylindrical base will be,

= 2 × 227 × 4.2 × 11.2 + 227 × 4.2 × 4.2

= 351.12 c m 2

The surface area of 50 cylinders,

= 50 × 351.12

= 17556 c m 2

Then the total cost will be,

= 17556 × 20100

= 3511.20

.
Thus the total cost of cardboard rate will be Rs.3511.20.
Therefore the correct option is 1.

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