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50 circular plates, each of radius $7 cm$ and thickness $0.5 cm,$ are placed one above another to form a solid right circular cylinder. What is the total surface area and the volume of the cylinder so formed?

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1408 cm 2

3850 cm 3

3850 cm 2

1408 cm 3

3050 cm 2

1400 cm 3

1008 cm 2

3000 cm 3

answer is A.

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Detailed Solution

Given that the number of plates is 50, radius of the plate is 7cm and its thickness is 0.5cm.
We have the following formulae,
The total surface area of cylinder =

2 π r h + r

The volume of the cylinder =

π r 2 h

h= (Thickness of 50 plates),

0.5 × 50

= 25cm
The total surface area of the cylinder will be,

= 2 × 227 × 7 (25 + 7) = 2 × 227 × 7 (32) = 44 × 32 = 1408 cm 2

The volume of cylinder will be,

= 227 × 7 × 7 × 25 = 50 × 77 = 3850 cm 3

Thus, total surface area is

1408 cm 2

and the volume is

3850 cm 3

.
Therefore the correct option is 1.

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