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Question

There is a retangular metal plate. I make a dent on the middle of the plate with a hammer to produce a conical depression. The top side of the metal is polished. What is the area of the metal polished?


A

Area of rectangle – Area of central circle + C.S.A of cone

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B

Area of rectangle + Area of central circle - C.S.A of cone

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C

Area of rectangle + Area of central circle + C.S.A of cone

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D

Area of rectangle + C.S.A of cone

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Solution

The correct option is A

Area of rectangle – Area of central circle + C.S.A of cone


Let us look at a side view of the metallic object.

The top view will be as shown below. The blue area is the area of conical depression seen from top.

The total surface area of the metal does not consist of the blue circle in the centre. The circular region is replaced by the curved surface of the conical depression.

The metal consists of the following surfaces-

Entire rectangular area except the circular portion depressed in the centre and the C.S.A of the conical region


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